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An experimental investigation of cathode erosion in high current magnetoplasmadynamic arc discharges

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An experimental investigation of cathode erosion in high current magnetoplasmadynamic arc discharges

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AN EXPERIMENTAL INVESTIGATION OF CATHODE EROSION IN HIGH
CURRENT MAGNETOPLASMADYNAMIC ARC DISCHARGES

by

Douglas A. Codron

_______________________

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ASTRONAUTICAL ENGINEERING)

August 2012

Copyright 2012 Douglas A. Codron

ii

Dedication Dedication Dedication Dedication

... ... ... ...to my parents for their undying love and support

iii

Acknowledg Acknowledg Acknowledg Acknowledgments ments ments ments

A number of people contributed in many ways to the completion of this dissertation. I do
not believe I would have come so far without their help.
I would first like to thank my advisor, Professor Dan Erwin, who brought me into
the department as a teaching assistant many years ago and provided the freedom to
pursue a line of research that most interested me. Thank you for allowing the frequent
visits to your office and providing the guidance necessary for the successful completion
of this work.
I would also like to extend a very special thank you to Dr. Keith Goodfellow who
has been a true role model during all facets of my doctoral experience. You have raised
the bar in my eyes as to what it means to do accomplished research. Thank you for
pushing this work a little further as you have set a precedent I will strive to emulate
throughout my future endeavors.
My sincere thanks to my lab mates John and Ning, who were not only great
sources of advice on all the hidden secrets of experimental research, but also made
coming to the lab fun. I will always look back with fondness at some of the silliness and
how it provided an escape during what could sometimes be a long and arduous process.
To Dr. Ryan T. Downey who paved the way for cathode research in the ASTE
Department: Thank you for your frequent visits, encouragement, and advice. I do not
iv
think I would have been able to get over some initial hurdles without it.
Another thank you to my fellow graduate student colleagues: Sam, Pedro, Daoru,
Steven, Ouliang, Brian, Gupta, Thada, Will, and Dayung all of whom were great
company along the journey. Also, thank you to the excellent staff: Dell, Marrietta, and
Ana who helped me navigate through the endless typical graduate school bureaucracy.
Dad, thank for bestowing in me since I was young a passion for science, as well
as the belief I could reach such heights. You have by and large made me the person I am
today. To my Mom and Louie: Thank you for always making me feel as though I was
working on something interesting and special. I’m sure there have been times when the
details of what I was working on were fuzzy, however, you both have been a constant
source of support and encouragement.
Lastly to Nadra, you have been my rock during all of this. You have changed my
perspectives on life in so many ways and I am a better person for it. Thank you for being
my biggest fan. I am very fortunate to have you in my life. I love you.

v

Table of Contents Table of Contents Table of Contents Table of Contents

Dedication ii

Acknowledgments iii

List of Figures vii

List of Tables xiii

Abbreviations and Symbols xiv

Abstract xvi

Preface xviii

Chapter 1: Introduction 1

Chapter 2: The MPD Thruster and Cathode Erosion 4
2.1 Solid Cathode Operation 6
2.2 The Multichannel Hollow Cathode 9
2.3 Thermionic Emission and the Role of Temperature 11
2.4 Physical Processes in Thoriated Tungsten Cathodes 13
2.5 Regions of the Cathode and Near-cathode Plasma 18
vi
2.6 Ionization 20
2.7 Mechanisms of Cathode Erosion 25

Chapter 3 Review of MPD Cathode Research 30

Chapter 4 Role of This Work 46

Chapter 5 Research Methodology 48
5.1 Propellant 54
5.2 Optical Pyrometery 54
5.3 Langmuir Probe 57
5.4 Scanning Electron Microscope (SEM) 58
5.5 CCD Camera Diagnostics 58

Chapter 6 Experimental Results 62
6.1 Optical Pyrometer Cathode Surface Temperature Profiles 62
6.2 Langmuir Probe Data 68
6.3 Discharge Current/Voltage Characteristics 76
6.4 Cathode Surface Topography and Composition 80
6.5 Charged Couple Device (CCD) Camera Temperature Profiles 88

Chapter 7 Conclusions and Future Work 106

Bibliography 109

Appendix A 116

Appendix B 121

vii

List of Figures List of Figures List of Figures List of Figures

Figure 1 A Model of an MPD Thruster 5
Figure 2 A Solid Rod Cathode 7
Figure 3 A Thoriated Tungsten Cathode (pre-discharge) 9
Figure 4 A Thoriated Tungsten Cathode After 5 Hours of Operation 9
Figure 5 Varying Designs of a MCHC 10
Figure 6 Temperature Dependence on Work Function
in Hollow Cathodes

13

Figure 7 Dependence of Work Function on the Density of
Adsorbed Thorium

15

Figure 8

Dependence of Work Function on Surface Coverage

15

Figure 9 Diagram of the Cathode and Near-cathode Plasma Regions 19
Figure 10 An Inelastic Collision Between Particles 20
Figure 11 Ionization Energy Potentials for Prospective EP Propellants 23
Figure 12 Evaporation Rate vs. Temperature of Tungsten 27
Figure 13 Relative Ion Intensity vs. Temperature 28
Figure 14 Front View of the Vacuum Chamber 50
Figure 15 Side View of the Initial Anode/Cathode Arrangement 50
viii
Figure 16 A General Schematic of the Experimental Setup 51
Figure 17 Voltage-Current Characteristic of a DC Low Pressure
Electrical Discharge Tube

52
Figure 18 Current Source and High Voltage Supply Decoupled
by a Blocking Diode

54

Figure 19 A Comparison of Optical Pyrometer and Thermocouple
Temperature Measurements
56

Figure 20 Circuit Diagram of the Langmuir Probe Setup 57
Figure 21 A Schematic of the CCD Camera Setup 59
Figure 22 Change of Cathode Temperature with Distance in a High
Voltage/Low Current Discharge (Glow Discharge)
63

Figure 23 Axial Temperature Profile of a Cathode in a
High Voltage/Low Current Arc Discharge with
Changing Pressure and Mass Flow Rate

63

Figure 24 Dependence of Peak Cathode Temperature on
Discharge Current

64
Figure 25 Dependence of Peak Cathode Temperature on
Discharge Power

65
Figure 26 Cathode Axial Temperature Profile with Changing Current
at 400 sccm

66
Figure 27 Cathode Axial Temperature Profile with Changing Current
at 450 sccm

66
Figure 28 Cathode Axial Temperature Profile with Changing Current
at 500 sccm

67
Figure 29 Cathode Axial Temperature Profile with Changing Current
at 600 sccm

67
Figure 30a Sample Langmuir Probe Trace (Near Cathode Plasma) 69
Figure 30b Sample Langmuir Probe Trace (Far Cathode Plasma) 70
ix
Figure 31 Electron Temperature vs. Discharge Current 71
Figure 32 Electron Temperature vs. Mass Flow Rate 72
Figure 33 Electron Density vs. Discharge Current 73
Figure 34 Electron Density vs. Mass Flow Rate 74
Figure 35 Plasma Potential vs. Discharge Current 75
Figure 36 Plasma Potential vs. Mass Flow Rate 76
Figure 37 Discharge Voltage vs. Discharge Current 77
Figure 38 Discharge Voltage vs. Mass Flow Rate 78
Figure 39 Discharge Resistance vs. Mass Flow Rate 78
Figure 40 Discharge Power vs. Mass Flow Rate 79
Figure 41 Discharge Resistance vs. Discharge Current 80
Figure 42(A) The Surface of an Unused Thoriated Tungsten Cathode at
250× Magnification
82

Figure 42(B) A Thoriated Tungsten Cathode (Upstream of Tip) After 2
Hours at 250× Magnification

82
Figure 42(C) A Thoriated Tungsten Cathode (Near the Tip) After 2
Hours at 250×Magnification
82

Figure 42(D) A Thoriated Tungsten Cathode (Near the Tip) After 2
Hours at 650× Magnification
82

Figure 42(E) A Thoriated Tungsten Cathode (at the tip) After 4.5
Hours at 160× Magnification
83

Figure 42(F) A Thoriated Tungsten Cathode (at the tip) After 4.5
Hours at 650× Magnification
83

Figure 42(G) A Thoriated Tungsten Cathode (at the tip) After 4.5
Hours at 1500× Magnification
83

x
Figure 42(H) A Thoriated Tungsten Cathode After 8
Hours at 35× Magnification

83
Figure 42(I) A Thoriated Tungsten Cathode After 8
Hours at 85× Magnification

84
Figure 42(J) A Thoriated Tungsten Cathode After 8
Hours at 450× Magnification

84
Figure 42(K) A Thoriated Tungsten Cathode After 8
Hours at 600× Magnification

84
Figure 42(L) A Thoriated Tungsten Cathode After 8
Hours at 850× Magnification

84
Figure 43 EDS Spectrum of an Unused Thoriated Tungsten
Cathode

86
Figure 44 EDS Spectrum of a Thoriated Tungsten Cathode
After 2 Hours

87
Figure 45 EDS Spectrum of a Thoriated Tungsten Cathode
After 4.5 Hours

87
Figure 46 EDS Spectrum of a Thoriated Tungsten Cathode
After 8 Hours

88
Figure 47 2D Image of Measured Intensity Distribution
of a Thoriated Cathode

89
Figure 48 Thoriated Tungsten Cathode Axial Temperature Profile
After 2 Hours

89
Figure 49 Thoriated Tungsten Cathode Axial Temperature Profile
After 4 Hours

90
Figure 50 Thoriated Tungsten Cathode Axial Temperature Profile
After 6 Hours

90
Figure 51 Thoriated Tungsten Cathode Axial Temperature Profile
After 8 Hours

91

Figure 52 488 nm Bandpass Filtered Argon Line Intensity
Contours for a Tungsten Cathode Tip After 2 Hours
at 60 A and a Mass Flow Rate of 500 sccm
92

xi
Figure 53 488 nm Bandpass Filtered Argon Line Intensity
Contours for a Tungsten Cathode Tip After 8 Hours
at 60 A and a Mass Flow Rate of 500 sccm

93

Figure 54 Thoriated Tungsten Cathode Axial Temperature Profile
at 30 Amps

93

Figure 55 Thoriated Tungsten Cathode Axial Temperature Profile
at 40 Amps

94
Figure 56 Thoriated Tungsten Cathode Axial Temperature Profile
at 50 Amps

94
Figure 57 Thoriated Tungsten Cathode Axial Temperature Profile
at 60 Amps

95
Figure 58 Cathode Peak Wall Temperature vs. Time 95
Figure 59 Cathode Wall Temperature vs. Time at Various Locations 96
Figure 60 Pure Tungsten Cathode Axial Temperature Profile
at 500 sccm

97
Figure 61 Pure Tungsten Cathode Axial Temperature Profile
at 640 sccm

98
Figure 62 Pure and Thoriated Tungsten Cathodes with Notable
Erosion at the Location of Maximum Temperature
on the Pure Tungsten Cathode After 4 Hours

98
Figure 63 Cathode Material Evaporative Mass Loss vs. Time 99
Figure 64 Pure Tungsten Cathode Radius vs. Distance
From the Initial Tip

99
Figure 65 Thermionic Electron Emission Current Density
vs. Distance From the Cathode Tip

100
Figure 66 Temperature vs. Thermionic Current Density 101
Figure 67(A) Thermionic Current Density vs. Distance From the
Cathode Tip at 60A After 2 Hours

104
Figure 67(B) Thermionic Current Density vs. Distance From the
Cathode Tip at 60A After 4 Hours
104
xii
Figure 67(C) Thermionic Current Density vs. Distance From the
Cathode Tip at 60A After 6 Hours

104
Figure 67(D) Thermionic Current Density vs. Distance From the
Cathode Tip at 60A After 8 Hours

104
Figure B.1 Diagram of a Hall Stationary Plasma Thruster 122
Figure B.2 Diagram of the Underlining Processes in an Ion Thruster 124
Figure B.3 Diagram of an Arcjet Thruster 126
Figure B.4 Diagram of a Pulsed Inductive Thruster (PIT) 128
Figure B.5 Diagram of the Variable Specific Impulse
Magnetoplasma Rocket

130
Figure B.6 Diagram of a Solid-Core Nuclear Thermal Rocket 134
Figure B.7 Major Components of a Particle-Bed Nuclear Rocket
Engine

135
Figure B.8 Major Components of a Liquid-Core Nuclear Thermal
Rocket Engine

136
Figure B.9 An Open-Cycle Gas-Core Nuclear Rocket Engine 137
Figure B.10 A Closed-Cycle Gas-Core Nuclear Rocket Engine 138
Figure B.11 A Conceptual Design of a Nuclear Pulse Rocket 139

xiii

List of Tables List of Tables List of Tables List of Tables

Table 1 Ionization Energy Requirements for Typical EP 23
Propellants at Varying Ionization Levels

Table 2 Relationship Between Electron Temperature and 24
First Ionization Energy and the Resulting Dominating
Ionization Process

Table 3 Experimental Data for a Thoriated Tungsten Cathode 105
at 0.6 kPa

Table A.1 Thruster Performance by Various Research Groups 117

xiv

Abbreviations and Symbols Abbreviations and Symbols Abbreviations and Symbols Abbreviations and Symbols

γ
bd
thorium diffusion rate (µg/cm
2
s)
Γ
W
mass loss rate per unit area
∆V velocity change (m/s)
ε
0
permitivity of free space (C
2
/N/m
2
)
ε emissivity
θ scattering angle or angle relative to the surface
λ wavelength (nm)
λ
D
Debye length (m)
λ
if
central wavelength (nm)
σ surface density (atoms/cm
2
)
σ
0
number surface density at minimum work function
τ
0
transmittance
φ work function (eV)
φ
eff
effective work function (eV)
a
0
atomic unit of length
A
R
Richardson coefficient (A/m
2
/K
2
)
A
s
probe collection area (mm
2
)
B magnetic field (tesla)
c speed of light (m/s)
D
bd,o
constant pre-exponential factor
e electron charge (C)
E
bd
activation energy (kJ/mole)
E
c
electric field (V/m)
E
i
ion energy (eV)
E
m
maximum energy transferred in a collision (eV)
f surface coverage
g
E
acceleration of gravity on Earth (m/s
2
)
g
i
ion statistical weight
g
0
ground state degeneracy
h Planck’s constant (J·s)
I energy needed for ionization from ground state (eV)
I
sat
ion saturation current (A)
I
sp
specific impulse (s)
xv
j current density (A/m
2
)
k
B
Boltzmann constant (J/K)
k
i
direct ionization rate coefficient
k
i
s
stepwise ionization rate coefficient
L
λ
*
source radiance (W·sr
-1
m
-2
)
L
bλ
blackbody radiance (W·sr
-1
m
-2
)
m mass (kg)
m
w
molecular mass of tungsten
M
0
total spacecraft mass (kg)
M
B
burnout spacecraft mass (kg)
M
p
spacecraft propellant mass (kg)
n
e
electron density (#/cm
3
)
n
Th
density of thorium (kg/m
3
)
p
W
vp
vapor pressure of tungsten (kg/(m·s
2
))
T temperature (K)
T
e
electron temperature (eV)
T
i
ion temperature (eV)
T
c
cathode temperature (K)
V
bias
applied voltage to Langmuir probe (V)
V
R
voltage across the resistor (V)
Z
ν
number of valence electrons

xvi

Abstract Abstract Abstract Abstract

Since the early to mid 1960’s, laboratory studies have demonstrated the unique ability of
magnetoplasmadynamic (MPD) thrusters to deliver an exceptionally high level of
specific impulse and thrust at large power processing densities. These intrinsic
advantages are why MPD thrusters have been identified as a prime candidate for future
long duration space missions, including piloted Mars, Mars cargo, lunar cargo, and other
missions beyond low Earth orbit (LEO). The large total impulse requirements inherent of
the long duration space missions demand the thruster to operate for a significant fraction
of the mission burn time while requiring the cathodes to operate at 50 to 10,000 kW for
2,000 to 10,000 hours. The high current levels lead to high operational temperatures and
a corresponding steady depletion of the cathode material by evaporation. This
mechanism has been identified as the life-limiting component of MPD thrusters.
In this research, utilizing subscale geometries, time dependent cathode axial
temperature profiles under varying current levels (20 to 60 A) and argon gas mass flow
rates (450 to 640 sccm) for both pure and thoriated solid tungsten cathodes were
measured by means of both optical pyrometry and charged-coupled (CCD) camera
imaging. Thoriated tungsten cathode axial temperature profiles were compared against
those of pure tungsten to demonstrate the large temperature reducing effect lowered work
function imparts by encouraging increased thermionic electron emission from the cathode
surface. Also, Langmuir probing was employed to measure the electron temperature,
xvii
electron density, and plasma potential near the “active zone” (the surface area of the
cathode responsible for approximately 70% of the emitted current) in order to
characterize the plasma environment and verify future model predictions.
The time changing surface microstructure and elemental composition of the
thoriated tungsten cathodes were analyzed using a scanning electron microscope (SEM)
in conjunction with energy-dispersive X-ray spectroscopy (EDS). Such studies have
provided a qualitative understanding of the typical pathways in which thorium diffuses
and how it is normally redistributed along the cathode surface.
Lastly, the erosion rates of both pure and thoriated tungsten cathodes were
measured after various run times by use of an analytical scale. These measurements have
revealed the ability of thoriated tungsten cathodes to run as long as that of pure tungsten
but with significantly less material erosion.

xviii

Preface Preface Preface Preface

In wake of the cancellation of the Constellation program, NASA will oversee a
fundamental change in American space policy. As part of this change in focus, President
Obama has presented NASA with the bold challenge of becoming an engine of
innovation, and the catalyst for an ambitious new space program [45]. With an added 6
billion dollars to NASA’s budget over 5 years, an aggressive shift in priorities are
encouraging the development of advanced propulsion engines with the clear goal of
carrying human beings further and faster into space [45]. Such ambitions will ultimately
lead to further exploration of the solar system and the manned exploration of Mars. In
order to achieve the challenging objectives laid out by President Obama, a host of
technological advances will be necessary. Of utmost importance will be the development
of the advanced propulsion systems capable of providing significantly reduced transit
times at lower costs.

1

Ch Ch Ch Chapter 1 apter 1 apter 1 apter 1

Introduction Introduction Introduction Introduction

A proposed mission to Mars using chemical propulsion can take upwards of two and a
half years roundtrip [3]. A mission of that order would be impractically long and ridden
with danger. The physical effects of exposure to high-energy cosmic rays and prolonged
low gravity can be potentially hazardous to the crew. Also, the associated costs of an
exceedingly large propellant supply and a robust life support system can dampen the
prospects of any proposal. Due to the prospect of shortened trip times, developing a
spacecraft with high propellant exhaust velocities and in turn high specific impulse (I
sp
) is
an attractive effort if a mission of this type is to be attempted.
Beginning in 1957 with the launch of the first artificial satellite, Sputnik, chemical
rockets have been used almost exclusively to transport payloads throughout the solar
system. Yet, the performance and speed limitations inherent of chemical rockets can be
observed in any proposed interplanetary mission. To illustrate, let us examine a
hypothetical manned mission to the planet Mars: At nearest to the Earth, Mars is
approximately 5.4 × 10
7
km.

However, the actual distance our spacecraft would be
required to navigate would be significantly further. In fact, basic orbital mechanics along
with an energy budget analyses demonstrates that launching upon closest proximity
2
would not be optimal. In this case, the ideal path would be more tantamount to a
Hohmann transfer trajectory [3], thus making the actual distance traveled over 2 × 10
8

km.
Fully aware of the distances between the two planets an evaluation of the
available propulsive capability is needed. The performance of a rocket is measured by its
ability to change the magnitude of its speed in a given direction by the ejection of mass at
a characteristic velocity. That change in the magnitude of the speed, ∆V, can be
expressed from the rocket equation as:

Δ V g I ln(M / M )
E sp 0 B
= , (1.1)

where g
E
is the gravity imparted on the spacecraft by the Earth, I
sp
is the specific
impulse, and M and M
0 B
are the total spacecraft and burnout masses respectively. The
Δ V required to travel to Mars (not including launch) is approximately 5.7 km/s. Today’s
more powerful chemical rockets are only capable of specific impulses up to 460 sec and
exhaust velocities of about 4.5 km/s, while current state of the art electric propulsion is
reaching I
sp
’s of about 4,000 sec and exhaust velocities of about 39 km/s [13]. Using,

M M 1 e
p 0
V
I g
sp E
= - 







- Δ
(1.2)

we see that to reach Mars, chemical rockets require on the order of 16 times more
propellant mass than electric propulsive thrusters. With the cost of roughly $22,000 [22]
3
for every kg launched to low Earth Orbit (LEO), mission planners can expect to save on
the order of millions of dollars in propellant costs when opting to use electric propulsion.
A strong candidate for a manned mission to Mars, the magnetoplasmadynamic
(MPD) thruster, is capable of meeting the scientific and technological challenges
demanded of this endeavor. With an I
sp
on the order of 3000-5000 s, exhaust velocities
of over 100 km/s [13], and relatively high thrust (in the case of electric propulsive
thrusters), MPD thrusters have the potential to significantly reduce transit times.
Unfortunately, this added benefit is crippled by thrust still incapable of exceeding levels
higher than about 100 N. As a consequence, MPD thrusters are expected to withstand
thousands of hours of use while simultaneously experiencing high operational
temperatures.
Due to the total impulse requirements inherent of the long duration space missions
typical of MPD thrusters, it has been recognized that the MPD operational life
requirement would be a significant fraction of the mission burn time (on the order of
2,000 to 10,000 hours [52]). However, operating for such prolonged periods will
continually expose the cathode to current levels in the range of tens of kiloamps. Such
continuously high current levels lead to high operational temperatures, thus ensuring
depletion of the cathode, which has been identified as the component most responsible
for limiting thruster lifetime. It is for this reason that physical insight into the most
destructive modes of cathode operation (the initial ignition of the discharge and the
subsequent material evaporation) are of much value. Continuing on this path, it is the
goal of this dissertation to develop a better understanding of the underlining processes
contributing to the erosion of these devices.
4

Chapter 2 Chapter 2 Chapter 2 Chapter 2

The MPD Thruster and Cathode Erosion

Traditionally, the definition of electric propulsion has been divided into three distinct
categories [29]:

• Electrothermal propulsion ─ Electrical energy is used to heat the propellant flow
by heat transfer from electrically heated surfaces or by direct heat deposition in
the flow itself.

• Electrostatic propulsion ─ The propellant is accelerated by direct application of
electric body forces to ionized particles.

• Electromagnetic propulsion ─ Electrical currents generated within the propellant
interact with magnetic fields to provide an accelerating force on the charged
particles.

Belonging to the third category, the MPD thruster is commonly classified as an
electromagnetic device.
5
Generally, an MPD thruster consists of a central rod cathode constructed of a high
melting point metal such as tungsten or tantalum which is often sintered with a low
percentage content of thorium (in order to effectively reduce the cathode material work
function and encourage increased thermionic electron emission). Surrounding the
cathode is typically a concentric anode also assembled from metal capable of
withstanding high temperature. Propellant gas is introduced through the cathode (hollow
cathode) or through the inter electrode gap and is subjected to a high voltage.
Subsequently, a high current arc is struck between the anode and cathode which breaks
down and ionizes the gaseous propellant.

A directed Lorentz force (J × B) resulting from the interaction between the azimuthal
magnetic field and the axial electric current acts to accelerate the quasi-neutral plasma
( + )
( + )
(─)

j
z

j
r

j
z

j
r

neutral
plasma
F
z
= j
r
B
θ

F
z

F
r
= -j
z
B
θ

F
r

F
F
B
θ

Figure 1: A Model of an MPD Thruster
propellant
propellant
6
both axially outward (often termed the “blowing” force) and radially inward (“pumping”
force) generating thrust. Often in low-powered thrusters (<500 kW), a solenoid magnet
surrounding the anode provides additional radial and axial magnetic fields that can help
stabilize and accelerate the plasma discharge resulting in an applied magnetic field
several times larger than the “self field” scenario. An illustration of the active forces
within an MPD thruster can be seen in figure 1.

2.1 2.1 2.1 2.1 Solid Cath Solid Cath Solid Cath Solid Cathode ode ode ode Operation Operation Operation Operation

Hollow cathodes are capable of operating with a lower voltage drop and a higher
maximum current density than traditional solid rod cathodes [15]. It is due to these
intrinsic advantages that there has been an increased focus on MPD thruster performance
studies which utilize hollow cathode geometries. However, the fundamental mechanisms
of cathode erosion (i.e. sputtering, undesired chemical reactions, and the evaporation of
cathode material) are near identical for both solid and hollow configurations. Due to a
largely more simplified solid cathode manufacturing process, this work will focus on a
series of experimental works exclusively on the solid variety. The following discussion
will illustrate the physical processes inherit of solid rod cathodes.
In these studies, cold (room temperature) gas (argon in this case) is introduced
symmetrically around and slightly downstream of the base of the cathode. Having been
recently accelerated in the cathode space-charge sheath, primary electrons emitted from
the cathode excite and ionize the neutral gas. After a series of collisions with heavy
particles and other electrons, the electrons reach thermal equilibrium and a quasi-neutral
7
and highly ionized plasma exits downstream of the cathode as seen in figure 2. Having
been formed from collisions with heavy particles, a significant fraction of migrating ions
are accelerated through the sheath potential drop and collide with the cathode surface,
depositing heat. This process continues to warm the cathode and a balance between
heating through ion bombardment and cooling through significant thermionic emission is
attained [17]. It is due to the high operating temperatures needed for thermionic emission
and characteristic of stationary cathode modes that a certain degree of mass loss is
guaranteed and is to some degree unavoidable.

+
─
Neutral Gas
Flow
Ions
Collision Ionization Active Zone Emitted
Electrons
Electron
Cathode
Anode
Highly Ionized
Plasma

Figure 2: A Solid Rod Cathode

In order for current continuity to take place in the interface between the cathode
8
and the plasma, a substantial number of electrons must be transmitted via thermionic
emission with approximately 70% originating from a region known as the active zone
during steady-state operation. In pulsed and low duty cycle applications, or during the
start up phase of continuous operation; the cathode remains relatively cold and a small
current flows via enhanced field emission from the cathode through the plasma. Since
the current cannot be sustained solely by thermionic emission, the current is maintained
by a number of very small and highly mobile emission sites (spots) (10
-4
to 10
-2
cm) [34]
in which the local temperature can be as high as the boiling temperature of the cathode
material within the spot attachment areas. As one emission site is rapidly heated, an
explosive release of cathode vapors and electrons occur followed by the appearance of a
new emission site at a nearby location [52]. After about 10
-4
seconds, the small primary
spots may transform into larger spots (10
-3
to 10
-2
cm) with temperatures exceeding 3000
K [34]. Figures 3 and 4 show the progression of the matured cathode spots which
provide conditions for intensive thermal erosion mechanisms. These cathode spots are
characteristic of the start-up phase which is likely to be the most destructive phase of
cathode operation [54].
The damaging effects of operating a cathode for long periods in such a
“nonstationary” mode can be lessened by uniformly raising the cathode temperature by
means of an artificial cathode heating technique [23] (although the utilization of such an
approach presents notable engineering challenges in the case of high current arc
discharges). However, if developed, an artificial cathode heating technique can highly
reduce the formation of the tiny localized regions of high temperature. If a cathode is
externally heated, it is not necessary to provide its heating by the ion current. In such a
9

Figure 3: A Thoriated Tungsten Figure 4: A Thoriated Tungsten
Cathode (pre-discharge) Cathode After 5 Hours of Operation

case, the main function of the cathode layer is the acceleration of thermal electrons to
energies sufficient for ionization while sustaining the necessary level of plasma density.
Losses of charged particles in such thermal plasma systems are typically not significant,
resulting in low values of cathode voltage drop.
To lengthen MPD cathode survivability, the cathodes are typically constructed of
high melting temperature, low work function materials such as tungsten and tungsten
based alloys [39] (it is not uncommon for thoriated tungsten cathodes to often be used in
place of the pure variety). In addition at high temperatures, thorium can act to lower the
tungsten work function and provides diffuse thermionic current emission [53].

2.2 2.2 2.2 2.2 The The The The Mu Mu Mu Mul l l ltic tic tic tichannel Hollow Cathode hannel Hollow Cathode hannel Hollow Cathode hannel Hollow Cathode

Although usually more efficient than the solid variety, the single channel hollow cathode
(SCHC) has limitations when operating in a high discharge and low mass flow rate
plasma environment. A tradeoff inherent of SCHC’s in such conditions is that in order to
maintain the discharge, the inside diameter of the cathode must be increased. If the
diameter is not adjusted to compensate for the increased discharge current, significant
10
cathode erosion and the premature failure of the device is likely to occur. However,
increasing the diameter demands a correspondingly high increase in the gas flow rate.
This increase prevents the backward displacement of the active zone from reaching too
far inside the cathode. Such an increase may result in a large increase in discharge
voltage and may change the operating regime of the active zone [10] (instead of resting
inside the cathode the active zone will be shifted downstream more toward the tip).
However, by employing the use of a multichannel hollow cathode (MCHC), many of
these issues which plague the SCHC can be better avoided.

Figure 5: Varying Designs of a MCHC

An MCHC is usually composed either of a group of tightly packed rods (by far
the most common design) or a single rod fitted with several holes parallel to the central
axis as shown in figure 5. In the case of the former, the propellant is fed into the gaps
between the rods and each channel acts as an individual hollow tube cathode. By doing
so, the emission area increases significantly and enables a reduction in both current
density and surface temperature. Therefore, MCHC’s operate at lower temperatures than
SCHC’s with the same outer radius and current. Also, by dividing the gas flow into
several channels, MCHC’s operate with a lower voltage drop and higher maximum
11
current density than conventional single-channel hollow cathodes, while also managing
to function with extremely low gas flow rates [15].

2.3 Thermionic Emission and the Role of Temperature 2.3 Thermionic Emission and the Role of Temperature 2.3 Thermionic Emission and the Role of Temperature 2.3 Thermionic Emission and the Role of Temperature

Thermionic emission is the heat-induced flow of charge carriers from a surface or over a
potential-energy barrier and is characterized by the saturation current density. When
exposed to an arc discharge, emitted electrons can remain in the surface vicinity of a hot
cathode creating a negative space charge and preventing further electron emission.
However, this induced negative space charge can be transported out of the near vicinity
of the electrode by the applied electric field over the surface (also denoted the cathode
sheath), thus allowing the discharge to reach the saturation current density.
The rate of this charge carrier emission is given by the Richardson-Dushman
equation:








 ϕ
- =
T k
q
exp T A j
B
eff 2
R
, (2.1)

where A
R
is an empirical constant for the cathode material (120 A/cm
2
K
2
) for thoriated
tungsten [53], T is the cathode temperature, k
B
is the Botlzmann constant, and
eff
ϕ is the
effective work function given by

0
c
w eff
4
qE
πε
- ϕ = ϕ . (2.2)
12
Letting
w
ϕ and E
c
denote the work function (the minimum energy necessary to extract an
electron from the cathode surface) and the electric field respectively, this relation
represents the well-known Schottky effect, which describes the influence an electric field
at the cathode’s surface has on lowering the material work function. The dominating
effect of work function on surface temperatures can be seen in figure 6. As observed, a
small change in work function can relate to dramatically lower temperatures for a given
current density.
In the case of large electric fields and high temperatures, thermionic and field
emission make significant contributions to the emitted current. However, in the case of
low temperatures, electrons are able to escape the surface only quantum-mechanically by
“tunneling” (the field emission mechanism) and do not reach the saturation level
necessary for arc continuity. Fortunately for MPD thrusters, the potential barrier is not
drastically insurmountable due to the relatively high thermal energies of the electrons.
This mechanism referred to as thermionic field emission is characteristic of MPD
thrusters and is critical in the development of cathode hot spots [44].
Since the concept of thermionic emission is rooted in the synergetic effects of
both temperature and the electric field, these parameters are required to be at or above a
critical value to provide significant emission current. It should be noted that thermionic
field emission dominates other mechanisms in the case when T ≥ 3000 K and E
c
> 8 × 10
6
V/cm [34]. For the scenario of lower electron temperatures and the same high electric
field strength, it is the effective reduction of the potential barrier which is responsible for
current continuity.

13
Figure 6: A Plot Illustrating Temperature Dependence on Work Function for
Both 4 mm and 6 mm Diameter Hollow Cathodes [10]

2.4 Physical Processes in Thoriated Tungsten Cathodes 2.4 Physical Processes in Thoriated Tungsten Cathodes 2.4 Physical Processes in Thoriated Tungsten Cathodes 2.4 Physical Processes in Thoriated Tungsten Cathodes

The rate of electron emission and the magnitude of the work function on the surface of a
thoriated tungsten cathode are dependent on both the absolute temperature and the
surface coverage profile of thorium. However, such a profile is difficult to obtain due to
the challenges associated with cataloging the loss rate of thorium evaporated from the
surface and its contrasting diffusion replacement rate [4]. Complicating the analyses
further is the time dependent nature of continuous thorium surface migration.
14
Experiments beginning in the middle 1930’s [8, 38] demonstrated a method for
maximizing the electron emission capabilities of thoriated filaments. To achieve such a
condition, the filaments were heated for a few minutes until they reached a temperature
of roughly 2800 K, allowing a low concentration supply of thorium metal to materialize.
However, due to the high temperatures, the rate of evaporation well exceeded the rate of
incoming diffused material, hindering the accumulation of thorium on the surface. To
combat this effect, the filament was then constantly heated at lower temperatures
allowing some of the metallic thorium to diffuse to the surface of the filament where it
formed a monatomic layer of adsorbed film. The emitting body was said to be
“activated” at these lower temperatures (2000-2300 K) with a diffusion rate sufficiently
higher than the evaporation rate, and thus allowing for some surface coverage. Stable
operation was considered to be achieved at equilibrium [53].
The rate of which thorium metal is supplied to the surface by diffusion, γbd, is
given by









∂
∂
- =
y
n
D γ
Th
bd bd
, (2.3)

where the y-axis is normal to the surface and
Th
n is the density of thorium in the solid.
The bulk diffusion coefficient, Dbd, is given by

( )
c b bd o , bd bd
T k / E exp D D = , (2.4)
15

Figure 7: Dependence of Work Function on the Density of Adsorbed Thorium [20]

where E
bd
is the activation energy, T
c
is the cathode temperature, and
o , bd
D is a constant
pre-exponential factor.
It was originally assumed that the work function was solely a decreasing function
of surface coverage. However, later studies demonstrated that the work function reaches
a minimum at a given surface density and tends to increase upon over saturation [20].

Figure 8: Dependence of Work Function on Surface Coverage [53]
16
As seen in figure 7, all three trials show a minimization of the work function at a surface
density, σ = 4.2 × 10
14
atoms/cm
2
and then a steadying at roughly σ = 9 × 10
14
atoms/cm
2
.
We see this same trend in figure 8. The surface coverage, f, is defined by σ/σ
0
, where σ
is the number density of adsorbed thorium atoms and σ
0
represents the number density at
the minimum work function. Such a trend can be described by the following: The
electric dipole layer formed by the electropositive atoms of thorium diffused to the
surface of tungsten lowers the cathode work function, facilitating the escape of electrons
from the surface and allowing a lower operating temperature for the same emission rate.
As the coverage of thorium is increased, a series of three distinct surface structures are
observed which exhibit a decreasing crystallographic relationship with the substrate
lattice. It is through the occurrence of these structures that a correlation with the changes
in work function of the system can be observed [20]. “A 1×1 structure which is
pseudomorphic with the underlying tungsten surface starts to form before the c(2×2)
structure is complete. The change in work function with surface coverage is linear at low
coverages because there is little dipole-dipole interaction in the c(2×2) structure.
However, the 1×1 structure requires closer packing, which leads to more dipole-dipole
depolarization and a flattening of the work function curve. Further coverage results in a
c(2×2) structure with no long-range order and the nucleation of thorium into "islands”
[53].” Within these isolated areas the c(2×2) structure is considered perfect [20].
Generally, there is no consensus on the exact diffusion mechanism supplying
thorium metal to the surface [53]. Such ambiguity is likely the result of ineffectively
cataloging the relative contributions of crystal lattice diffusion and grain boundary
diffusion. In 1923, Langmuir [37] proposed that in an ordinary tungsten filament,
17
thorium diffused to the surface in a roughly uniform fashion through the tungsten crystal
lattice. He based this assumption on a general model of metal to metal diffusion
processes in which only atoms containing a certain amount of kinetic energy or potential
are allowed to make interchanges in position. Those atoms of suitable energy may reach
the surface forming an adsorbed film layer roughly a single atom in thickness, completely
covering the surface.
It was shown later [21] in examinations of diverse lots of thoriated tungsten wires,
that values of the diffusion and activation constants often varied widely from those
reported by Langmuir. It was proposed that the diffusion rate was affected by crystal
grain size and was particularly rapid along grain boundaries. Experiments observing the
emissive life of thoriated tungsten filaments showed that variations in thoria content
between identical filaments had little influence on length of life, whereas high
temperature flashes demonstrated large increases in tungsten grain size and significantly
longer lifetimes. Further studies demonstrated that activation rates for single crystal
filaments were much lower than that for polycrystalline filaments. In a reexamination of
the data, Langmuir concluded that the dominant mechanism at temperatures below 2400
K is grain boundary diffusion and at higher temperatures the lower activation rate could
be attributed to lattice diffusion.
In a subsequent electron microscope study [1], it was proposed that thorium
diffused to the surface by processes of “eruptions” from a relatively small number of
randomly located points. It was observed that such eruptions are the only manner in
which thorium arrives on the surface and the frequency of such eruptions increases with
temperature. During eruptions approximately all the thorium in a globule of thorium
18
oxide comes to the surface. Where a thorium oxide globule embedded in a mass of
tungsten represents a closed system in which

Th WO W ThO
2 2
+ ⇔ +

would be in equilibrium.
A notable trend was that eruptions were only witnessed to occur when the surface
concentration of thorium was only 40% or below the value necessary for optimum
thermionic emission. Such a scenario is due to the low contrast in brightness between the
eruption point and its surroundings and the high evaporation rate at higher activities.
Importantly, eruptions were twice as likely to appear on crystal faces as opposed to grain
boundaries [1]

2.5 2.5 2.5 2.5 R R R Regions of the Cathode and Near egions of the Cathode and Near egions of the Cathode and Near egions of the Cathode and Near- - - -c c c cathode Plasma athode Plasma athode Plasma athode Plasma

During the operation of a solid cathode there will exist a distinct set of regions each with
their own influence on the current conduction and energy transport throughout the
system. Within the cathode itself, the current is conducted exclusively by the migrating
electrons. Such electrons move freely until enough energy is supplied to thermionically
emit the electrons from the surface and an energy balance between ion impacts and
emitted electrons works to raise the cathode temperature. In general, only electrons with
sufficient thermal energy can overcome the large potential barrier. It is therefore
19

Figure 9: Diagram of the Cathode and Near-cathode Plasma Regions [52]

desirable to minimize the size of the potential barrier in an effort to decrease cathode
surface temperatures.
Located very near the surface is a region known as the sheath. At this location a
large potential gradient develops. As the electrons are repelled from the cathode and ions
are attracted, a thin layer of positively charged ions is formed effectively acting to screen
the discharge and thus limiting its potential from influencing the arc discharge. In the
case of MPD thrusters, the sheath is considered to be collisionless since the sheath is only
on the order of a few Debye lengths (λ
D
) and much less than the particle mean free path.
Because the plasma sheath does not perfectly shield itself, a small penetrating electric
field acts to accelerate the ions in the quasineutral plasma and forms a region known as
the presheath.
The plasma ions must be accelerated to a minimal velocity while maintaining
enough energy (Bohm energy) to maintain a stable sheath. Consequently, a region of
20
plasma near the surface that is heated by emitted electrons forms a region known as the
ionization zone. Ions attempting to leave the sheath edge must reach the Bohm energy if
they are to reach the free stream plasma. In the ionization zone there is a transition
between solely electron dominated current conduction and conduction with both electron
and ion components. Thermal and momentum boundary layers form between the
ionization zone and the free stream plasma as seen in figure 9.

2.6 2.6 2.6 2.6 Ionization Ionization Ionization Ionization

The development of any self-consistent model aimed at replicating the current conduction
mechanism and processes that influence plasma penetration depth, cathode temperature,
and cathode voltage drop, will be required to directly calculate the ionization and
excitation rates of the relevant states of the neutral atoms [43]. The characteristic
attributes of these excitation rates as determined by thermal and thermionic electron
conditions are crucial for modeling the continuum dynamics of the ions.

X e A A X + + → +
+
~

Figure 10: An Inelastic Collision Between Particles [30]

X
~
A X
e
-

A
+

21
Within a plasma environment, the energy required for ionization of neutral atoms is often
supplied by a series of inelastic collisions. Such collisions result from the transfer of
energy from the kinetic impacts of colliding particles, thus leading in a relocation of
internal energy to the charge carriers. This process is illustrated in figure 10.
In this research, the working gas (argon) is ionized via multi-step collisions from
electrons thermionically emitted from the cathode wall and from the collisions of thermal
electrons (those of high velocities in the upper part of the distribution) with the argon
atoms. Direct ionization may occur if a collision bent electron’s internal energy is
sufficiently large enough to initiate ionization in a single impact event. Electron particles
thermionically emitted and accelerated through the sheath potential drop and those in the
high energy tail of the distribution often fall into this ionization category. The direct
ionization rate coefficient is given by

( ) k T
8T
m
exp
I
T
i e
e
0
e
= - 





π
σ , (2.5)

where I is the energy necessary for ionization from the ground state and σ
0
=
Z
ν
πe
4
/I
2
(4πε
0
)
2
= 3·10
-16
cm
2
(for argon) is approximately the geometrical atomic cross
section with Z
ν
representing the number of valence electrons. Electron temperature is
given in energy units (eV).
However, it is often the case that a collision may only partly raise an atoms
internal electronic energy level. In such an occurrence an excited electron will transition
to a discrete and higher orbit (in accordance with a Rutherford–Bohr model) and may
22
only become ionized by the further cascade of inflowing electrons. This is known as a
stepwise ionization process and is represented by

( )
k
g
g
1
4
me
h T
exp
I
T
i
s i
0
0
5
10
3
e
3
e
≈





 - 





πε
, (2.6)

where h is the Planck’s constant and g
i
and g
0
is the statistical weight of the ions and
ground state particles respectively. Comparing the process of direct ionization with
stepwise ionization yields

( )
( )
k T
k (T )
g a
g
1
4
me
hT
I
T
i
s
e
i e
i 0
2
0 0
0
2
4
e
7/2
e
7/2
≈








≈






σ
π ε
, (2.7)

where a
0
is the atomic unit of length. This equation demonstrates the potentially faster
rate of ionization in the stepwise case. Figure 11 shows the first ionization energy
potentials of various propellants, while table 1 displays the ionization energy
requirements for typical electric propulsion propellants at varying ionization levels.
Factors which contribute to stepwise ionization include the duration in which an atom
remains in the excited state and the electron and neutral atom collision frequency. If the
time duration an atom is in the excited state is consistent with the electron-neutral atom
collision frequency, the neutral atom’s electrons have a higher probability of being
excited and an ionization event is more likely to occur.

23

Figure 11: Ionization Energy Potentials for Prospective EP Propellants [59]

Table 1: Ionization Energy Requirements for Typical EP Propellants
Propellant 1
st
Ionization
(eV)
2
nd
Ionization
(eV)
3
rd
Ionization
(eV)
Argon
15.76 27.63 40.74
Lithium
5.39 75.64 122.45
Xenon
12.13 21.21 32.12
Helium
24.59 54.42 -----------------
Hydrogen
13.6 ------------------- -----------------
24
Although the total energy needed for ionization is the same for both the direct and
stepwise case, it is often difficult to assess which process is preferable and which
contributes the most to the total rate of ionization. Since the statistical weight of
electronically excited neutral atoms is greater than that of free plasma electrons, it is
generally accepted that if the level of electronic excitation is sufficiently high, the
stepwise ionization process proceeds at a faster rate than that of direct ionization [58].
However, in the case of determining the probability of a given ionization process, the
relationship between electron temperature and ionization energy is crucial. Electron
temperatures significantly lower than the first ionization energy of the neutral have a
much higher probability of leading to a stepwise ionization event, while electron
temperatures of the higher variety will likely lead to the opposite process.
As shown, table 2 illustrates the relationship between electron temperature and the
first ionization energy, and tabulates the dominating ionization process.

Relationship

Dominating Ionization Process
T
e
<< I

Stepwise
T
e
≈ I

Both stepwise and direct are significant
contributors
T
e
>> I

Direct

Table 2: Relationship Between Electron Temperature and First Ionization Energy
and the Resulting Dominating Ionization Process

25
2.7 2.7 2.7 2.7 Mechanisms of Cathode Erosion Mechanisms of Cathode Erosion Mechanisms of Cathode Erosion Mechanisms of Cathode Erosion

Once introduced into a high current gaseous discharge, mass loss from the cathode can
occur due to variety of mechanisms. Major causes include: sputtering, evaporation of the
cathode material, the ejection of molten material, and undesired chemical reactions [50].
It is due to these dominant erosion mechanisms that cathode lifetime can be severely
limited.

Sputtering

In MPD thrusters, sputtering is driven by the momentum exchange of colliding ions and
the atoms of the cathode material. If enough energy is transferred to overcome the
surface binding force during impact, material from the surface will be deposited on the
walls of the cathode. The average number of atoms ejected from the surface during
impact is known as the sputter yield. The sputter yield is dependent on the colliding ion’s
energy, the mass of the ion, the mass of the atoms of the impacted material, and the
surface binding energy of the cathode bulk’s atoms. In order to calculate the amount of
sputtering, any model would have to take into account the fraction of atoms ejected from
the surface which find their way to another surface, the number of ions of a given energy
striking the cathode, and the number of atoms dislodged by a given ion of a certain
energy [61]. The energy transferred in such a collision process is given by

2 / sin E E
2
m
θ = , (2.8)
26
where θ is the scattering angle in the centre of mass system and
m
E is the maximum
possible energy transferred in a collision and

i
2
2 1
2 1
m
E
) M M (
M M 4
E
+
= , (2.9)

where M
1
and M
2
are the masses of the impinging ion and the target atoms respectively
and
i
E is the energy of the ions. The energies found in MPD thruster cathodes typically
fall into a sputtering class known as thermal spike sputtering which occur most frequently
with high energy and heavy incident particles [52].

Evaporation of Cathode Material

Hot-cathode erosion is primarily from the evaporation of cathode material, with the
evaporation of the cathode material being dependent on desorption and gas phase
reactions [52]. When the cathode evaporation rate exceeds the absorption rate, an overall
loss of mass occurs. The upper bound of mass loss rate per unit surface area,
W
Γ , is
described by [10]

( )
C
W
vp
2 / 1
c B
W W
T p
T k 2
m








π
= Γ , (2.10)

where
W
m is the molecular mass of tungsten,
B
k is Boltzmann’s constant,
C
T is the
27
cathode temperature, and ( )
C
W
vp
T p is the vapor pressure of tungsten as a function of the
surface temperature. Figure 12 shows the evaporation rate of tungsten as a function of
temperature.

Figure 12: Evaporation Rate vs. Temperature of Tungsten [25]

Ejection of Molten Material

For quasi-steady or pulsed operation, the current generally tends to concentrate within
small micro-spots on the surface. It is in these areas that the ejection of molten material
becomes a dominant cathode mass loss mechanism. The melting rate and total rate at
which material is removed from the melted bulk both contribute to this loss mechanism.
However, these rates are difficult to obtain due to the dependence on the magnitude of the
plasma pressure and the electrohydrodynamic forces on the liquid. It is the uncertainty of
the rate at which ejected material is transported through the surrounding plasma and the
challenge of determining particle trajectories which further complicate the analysis [52].
28
Chemical Reactions

In a high current discharge, tungsten can be oxidized by residual oxygen, water vapor, or
their products which are often present in the propellant impurities. Since many of these
products will have a higher vaporization pressure than pure tungsten, this can lead to high
rates of tungsten mass loss [52]. Often, the main products of the chemical reaction are
W
3
O
9
, W
2
O
6
, WO
3
, and WO
2
[57]. The effect temperature has on the magnitude of the
relative ion intensities can be seen in figure 13.

Figure 13: Relative Ion Intensity vs. Temperature [57]

29
The adsorption and dissociation of molecular oxygen on two distinct surfaces
leads to the oxidation of tungsten at low oxygen pressure. This interaction is
characterized by strong surface bonding in the first layer and considerably weaker
bonding in the second layer. For lower temperatures (~1300 K and below) tungsten
oxides form a layer on the surface which discourages the oxidation reaction, however, at
the higher temperatures relative to MPD thruster cathodes, the rate of formation of atomic
oxygen reaches a limit where it is nearly equal to twice the rate of impingement of
molecular oxygen on the surface [57]. At the highest temperatures the molecular oxygen
remains in contact with the surface long enough to be absorbed and then dissociated.

30

Chapter 3

Review of MPD Cathode Research

The essential elements of the underlining physics governing the operation of MPD
thrusters have been known for some time. However, prior to 1964, no device remotely
resembling a practical space thruster of the steady flow electromagnetic class yet existed.
Complications associated with the production and handling of ionized gas flows,
preserving electrode surfaces in the face of a harsh plasma environment, and achieving
satisfactory electromagnetic field strengths coupled with uniform geometries were but a
few of the challenges encountered during early MPD thruster development. Of the
issues, arguably, the most serious was (and still is) the very large and cumbersome power
supply [55].
Originally developed for ground-based power generation and wind tunnel type
test facilities, the massive preionizing equipment was quickly observed to be unadaptable
for space applications. Even if such technologies were applied to MPD thrusters,
drawbacks such as low density thrust and low efficiencies had to be surmounted.
Not too long after research into MPD thrusters was all but abandoned, significant
breakthrough developments quickly renewed interest in the field. Experiments on arcjet
31
thrusters showed that a drastic reduction in propellant mass flow followed by a drop in
pressure in the arc chamber could yield exceedingly high arc currents without serious
detrimental erosion to the electrodes [62]. High exhaust velocities were now achievable
and efficiencies reached as high as 50% [30]. With MPD thrusters approaching the
performance limits required, attention was directed toward extending the life of the
cathode as it was soon realized to be the life limiting component of the MPD thruster.
Therefore, to this date, the cathode is the most studied and examined component of these
devices.

Delcroix et al. ─ Laboratoire de Physique des Plasmas (1968-1978)
[14, 15, 16]

Pioneering experimental studies accomplished by Delcroix, Minoo, and Trindade from
1968-1978 at the Laboratoire de Physics des Plasmas demonstrated the ability of
MCHC’s to operate with a lower voltage drop, a reduced operating temperature, and a
higher maximum current density when compared to conventional single-channel hollow
cathodes. In addition, due to the added benefit of conducting more current and operating
at lesser gas flow rates, they demonstrated that MCHC’s can have potentially longer
lifetimes.
These researchers developed the concept of the “active zone”, which is taken to
be the region of the cathode wall supplying the majority of the emitted current (typically
in the range of 70-100%). They demonstrated that during normal conditions, gas fed
hollow cathodes exhibit at some location along the cylindrical wall a white hot active
32
zone and that a portion of the internal plasma column (IPC), penetrates inside the cathode
tube. They argued that the IPC length was a function of the cathode internal diameter
and the inner cathode gas flow rate. By either increasing the cathode diameter or
reducing the flow rate, it was found that the length of the IPC increased.
This group stressed, in the case of high discharge currents, the importance of the
cathode internal diameter being of adequate size. It was witnessed that if the inner
diameter did not conform to the size requirement, the current density could not be
maintained below the critical values and the lifetime of the cathode would be
significantly shortened. However, they warned that in the case of large diameters, the gas
flow rate must be heavily increased in order to prevent the backward displacement of the
active zone from reaching too far inside the cathode, resulting in a large increase of the
discharge voltage and a change in operating regime.
Qualitative arguments demonstrating the negative effect on voltage drop due to a
partial igniting of the channels of an MCHC were presented. They showed that when
operating a large diameter MCHC at low current, that a small number of channels are
ignited. It was shown that in order to increase the number of active and ignited channels,
the current must be increased up to the point where the current density is large enough to
ignite all the channels. If the condition of adequate current density is not satisfied, the
gas flow was shown to divide unevenly between the ignited and unlit channels and an
increase in the IPC among the ignited channels would result.

Comments:
Although largely experimental in nature and providing mostly qualitative relationships,
33
the work by Delcroix et al, undoubtedly demonstrated the benefits inherent of MCHC’s
when compared to SCHC’s. The ability of MCHC’s to operate at lower discharge
voltages and temperatures, as well as the prospect for longer cathode operational
lifetimes, has definitively made the case for future high current cathode research to be
rooted in their findings.

Babkin, Mithalev, et al. ─ Moscow (1975-1979) [5, 6]

Babkin and Mithalev were the lead members of a research group that were also interested
in studying the physical conditions inside a MCHC. Building off earlier work conducted
by Delcroix et al, they sought to alleviate the difficulties associated in determining the
plasma parameters in the small cross-sectional areas of the channels. Difficulties such as
diagnosing the magnitudes of the pressures, concentrations, temperature, and degree of
ionization in the plasma for various levels of discharge current plagued their early
experimental investigations. Yet, despite the associated challenges, additional
complexity was added when their work was focused on the use of alkali metals as
opposed to the more predictable noble gases.
The cathode of the plasma source was a bundle of 19 tungsten tubes with internal
and external diameters of 12 mm and 16 mm respectively. The tubes were constructed
from tungsten foil with a width of 25 mm and thickness of 0.05 mm and were extended 5
mm past the end of the tube. The anode, made from molybdenum, had an outlet diameter
of 60 mm. The working fluid was lithium supplied at a mass flow rate of 0.01 g/sec. In
34
addition, a coaxial plasma source with a power of 7 kW was used. A novel optical
system for observation consisting of a lens and mirror was utilized. This system formed
an image of the channel selected and magnified it an order of magnitude on the entrance
slit of a spectrograph. The contribution of the emission of the interelectrode plasma
column was taken into account by means of a monitoring tungsten rod, installed in one of
the adjacent channels. Lastly, the discharge current was varied from 50-500 A while the
voltage ranged from 10 to 15 V.
The spectroscopic investigations revealed that the concentration of electrons and
neutral atoms, as well as the plasma pressure in the active zone, were increasing functions
of discharge current. The average temperatures of the electrons and neutral atoms were
5500 K and 3000 K respectively. Also, it was found that the electron concentration in the
active zone depended weekly on the mass flow rate of the working fluid.

Comments:
As with many early studies on MCHC’s, the research conducted by Babkin and Mithalev
et al. did not focus on the development of any model for the plasma characteristics with
an MCHC and produced little in the way of quantitative results. However, this group
replicated some of the important findings uncovered by Delcroix et al. and demonstrated
MCHC’s ability to operate over a wide range of current. In addition, their research
exhibited techniques (i.e. a monitoring tungsten rod to measure interelectrode plasma
column emissivity and an elaborate optical system) useable for obtaining data from a
high temperature and harsh environment.

35
Polk et al. ─ NASA, JPL/Princeton University (1991-2003) [33, 52, 53]

In the early to middle 1990’s James Polk, among others, were interested in characterizing
the dominant mass loss mechanisms (i.e. sputtering, ejection of molten material, cathode
material evaporation, and evaporation of the products created in reactions between
cathode materials and propellant gases) that could lead to cathode failure in MPD
thrusters. In order to achieve this, he developed a method for analytically determining
the important environmental parameters that drive cathode erosion. Three significant
modeling regimes were introduced: The far-field plasma flow model, the near-cathode
plasma/surface model, and the cathode thermal model.
Polk employed a method known as the surface layer activation technique (SLA),
to measure erosion rates in both quasi-steady and steady-state discharges. By utilizing a
weak radioactive tracer in a thin surface layer of the cathode, it was revealed that the
amount of mass lost from the surface during operation can be accurately deduced from
the observable decrease in tracer activity. As a consequence, this method yielded very
accurate, spatially resolved, measurements of cathode mass loss.
In addition to the development of the SLA, Polk helped verify important
operating characteristics of high-current cathodes. He noted that during the start phase of
steady-state cathode operation, the cathode is subjected to a variety of destructive erosion
processes, and that for low current densities; the mass erosion rate is dominated by vapor
production and the ejection of small droplets in isolated emission sites. Therefore, at a
certain threshold current density, the overlapping temperature fields of adjacent emission
sites cause melting on a larger scale and the mass loss by droplet ejection increases
36
dramatically. Also, he observed that the thermionic emission from a hot cathode is an
inherently less destructive process than in the cold cathode case. He based this on the
idea of “hot spot” formation on the surface of cold cathodes. He argued that as the
cathode is introduced to the initial discharge, it is unable to generate the required current
through thermionic emission. Therefore, in order to overcome this deficiency, the current
is maintained within small regions at varying locations on the cathode surface. He
argued that an inconsistent heating process continues until a higher and more uniformly
distributed temperature is obtained and it is these locations of increased electron mobility
and intense heat which are responsible for a significant fraction of cathode material
erosion.

Comments:
Although the concept of hot spot formation as being a significant contributor of cathode
erosion was well known at the time, Polk nevertheless accurately catalogues many of the
dominant mass loss mechanisms in high current cathodes. By applying basic principals
such as: Using materials with low work functions, utilizing cathode additives, increasing
cathode emitting area, actively cooling and heating the cathode, etc., he has provided the
theoretical ground work for the development of phenomenological models representing
the processes which control mass loss rates in these devices.

37
Goodfellow ─ University of Southern California/JPL (1991-1996)
[24, 25, 26]

In the early 1990’s, Keith Goodfellow identified the operating characteristics of cathodes
in gaseous discharges with applications to electric thrusters. He characterized erosion
from evaporation as being the major life-limiting mechanism in steady-state cathode
operation. Therefore, the main focal point of his work was to evaluate cathode
temperature by use of a theoretical model of the cathode discharge and by using
experimental results to verify the model predictions.
In his work, Goodfellow employed a thermal model which was used to determine
the temperature distribution within the cathode, and a near-cathode plasma model, used to
determine the surface heat flux and current density. He proposed that the near-cathode
plasma could be described by a series of plasma regions (such as the sheath and the
boundary layers) allowing the individual regions to be linked, furthering the construction
of the near-cathode plasma model. A series of experiments were performed to
compliment the modeling work. Tests were conducted to simulate the discharge
characteristics within MPD thrusters. Different operating parameters were alternately
varied (i.e. thoriated tungsten cathodes as oppose to pure tungsten) and significant
variations in the cathode temperature distributions were observed.

Comments:
Focusing on high current solid rod cathodes, and utilizing models not incorporating the
work function distribution on thoriated tungsten cathodes or the relationship between the
38
arc attachment area and the sheath potential drop, Goodfellow demonstrates excellent
agreement between model predictions and experimental results for both low and high
pressure discharges. His model accurately predicts the resultant cathode temperature
profile for the experimentally verified arc attachment area and provides a more detailed
observation of the plasma and sheath regions.

Tikhonov et al. ─ Moscow Aviation Institute/NASA (1994-1998) [60]

In the mid to late 1990’s the Research Institute of Applied Mechanics and
Electrodynamics of the Moscow Aviation Institute (RIAME MAI) with the support of
NASA/JPL and Princeton University, conducted experimental studies on lithium based
MCHC’s. Initial studies were proposed to determine the mechanisms of cathode erosion
on both low and high powered thrusters (~30 and 200 kW). In addition, experimental
verifications of the impact of barium additives (a reduction of the tungsten electronic
work function from 4.5 to 2.1 eV was observed) on cathode lifetime were investigated.
The design of both thrusters incorporated a heater which preheated the cathode
surface to temperatures between about 1300 K and 1500 K. By doing so, a high and
evenly distributed initial cathode temperature could be obtained. In an attempt to obtain
equal current densities (~130 A/cm
2
), the 30 kW model employed a cathode and anode
outlet diameter of 24 mm and 70 mm respectively. While the 200 kW thruster’s cathode
and anode had diameters of 55 mm and 160 mm. Previous experimental studies of 30
kW thrusters have shown that a multicavity cathode assembled from tightly packed 2-4
mm tungsten rods are a reasonable configuration. Discharge current was varied from 700
39
to 800 A for the 30 kW thruster and 2.9 to 3 kA for the 200 kW thruster.

Comments:
The experimental results confirmed most of the findings of previous studies and provided
mostly qualitative data emphasizing the mechanisms of cathode erosion. A comparison
of a lithium thruster without and with barium additives revealed approximately a 13.5 %
reduction in cathode temperature and an 8.4 % decrease in discharge voltage (while
operating at the same discharge current) in the latter case. These results demonstrated the
increased emissive properties of the cathode when barium is added to the main plasma
producing substance.

Mikellides et al. ─ NASA/JPL/Cal Tech (2001-2005) [41, 42, 43]

Beginning in the early 2000’s and building upon previous work undertaken at Ohio State
University, Mikellides and his research group sought to develop a global model of the
cathode plasma that can be used routinely to access the life and performance of ion
engine orificed hollow cathodes. In this pursuit, the IROrCa2D (Insert Region of an
Orificed Hollow Cathode) was developed. As a 2D axisymmetric, time dependent code
simulating the plasma inside the emitter region of a low current orificed hollow cathode,
the IROcCa2D code was one of two theoretical models developed. The second model,
OrCa2D, is also a 2D axisymmetric time dependent code that simulates the plasma and
neutral gas dynamics in the emitter, orifice, keeper, and plume regions. However, unlike
the IROrCa2D code, the OrCa2D can work independently of boundary inputs obtained
40
from experimental data.

Comments:
The codes developed by Mikiellides et al. were used in the development of the cathodes
for NASA’s Solar Electric Propulsion Technology Applications Readiness (NSTAR)
project. Such cathodes were successfully implemented on NASA’s Deep Space 1
mission as both the main ion-engine plasma source cathode and the neutralizer cathode.
Although primarily developed to model the physics inside a Xenon-fed low current
orificed hollow cathode, recent work at the University of Southern California has
demonstrated the ability of these models to be adapted for use in both SCHC’s and
MCHC’s.

Cassady ─ Princeton University (2001-2006) [10, 11]

Leonard Cassady, of the Electric Propulsion and Plasma Dynamics Laboratory (EPPDyL)
at Princeton University conducted experimental and theoretical studies investigating
lithium-fed multi-channel and single channel hollow cathode arc attachment. The
primary focus of his work was to identify the current conduction mechanism and the
conditions which determine the plasma penetration depth, cathode temperature, and
cathode voltage drop. To achieve this, four lithium-fed SCHCs (with inner diameters of
2, 4, 6, 8 mm) and a MCHC (19 - 1 mm channels in a 10 mm diameter rod) were
employed and were exposed to mass flow rates of 0.2 - 4.0 mg/s and currents of 5 - 210
A. Cathode voltage and temperature profile measurements along with comparisons of
41
plasma penetration depth as a function of current revealed that the plasma penetration
length increases with current and that the peak cathode temperature is independent of
mass flow rate, dependent on channel diameter, and weakly dependent on current.
In his work, Cassady attempted to provide a theoretical working model that
predicted measurable properties such as the cathode voltage drop, the plasma potential at
the cathode tip, cathode temperature, and plasma penetration depth in both lithium-fed
SCHC’s and MCHC’s. To accomplish this, the model represented these properties as a
function of channel diameter, mass flow rate, current, and, for the MCHC, the number of
channels and overall cathode diameter.

Comments:
Cassady’s work was undertaken with the intention of constructing a self-consistent model
that unlike any previous models did not require experimental data as inputs, but rather
could be used to make independent calculations which could be compared to the
experimental data. However, the goal of constructing a model without experimentally
realized boundary conditions was and still is a considerable challenge, and to date no
complete self-sufficient model of SCHC or MCHC cathode operation has been
developed. Even an all inclusive model of SCHC operation which accurately accounts
for the relation between discharge voltage, mass flow rate, and IPC penetration depth has
yet to be completed. Therefore, in order to develop a working model of an MCHC,
Cassady had to simplify the model by assuming all of the channels of the MCHC have
the same diameter, mass flow rate, and current. By doing so, the mass flow rate and
current in each channel could be calculated by the total mass flow rate and current
42
divided by the number of channels. Although not an unreasonable assumption, it fails to
take into consideration two important characteristics of MCHC’s:
• The uneven velocity profile inside the cathode walls. Since the particles on the
outer edge of the profile will move at lower velocities compared to those in the
center, each channel will have a different mass flow rate, and therefore a different
IPC profile.
• The power lost to thermal radiation and conduction is not equally attributed to
each channel. Radiant heat transfer from the inner channels to adjacent channels
and radial variations in the temperature of the channels (which have a portion of
their surface exposed to the external environment) both contribute to the uneven
diffusion of thermal radiation.

Nevertheless, it is not clearly evident that the omission of the above assumptions will
have a significant effect on disproving the experimental trends linking cathode voltage,
current, temperature profiles, and ionization fraction in SCHC’s and MCHC’s.

Downey ─ University of Southern California (2004-2008) [17, 18]

At the University of Southern California, Ryan Downey investigated both the theoretical
and experimental aspects of high current hollow cathode arc attachment. His work was
focused mainly around SCHC’s and was mostly concerned with the thermal loading of
the cathode. A high-current discharge was maintained with a 10 mm tungsten cathode at
a stable operating point of 40 sccm mass flow rate, 35 amps, and 37 volts. Unfortunately,
43
equipment failures limited the range and quantity of experiments which were expected to
profile the plasma potential and density at the exit plane of the cathode. A summary of
some his significant findings are given:

Magnitude of Peak Temperature
• The magnitude of the peak temperature along a hollow cathode is to some degree
dependent upon mass flow rate (approximately linear related), with higher flow
rates resulting in higher peak temperatures. (The conclusion that the magnitude of
the peak temperature is dependent upon the mass flow rate is in contrast with
Cassady’s work. While plasma penetration depth was discovered to be a function
of mass flow rate, he shows that the peak temperature is not correlated.)
• The magnitude of the peak temperature along the hollow cathode is dependent
upon discharge current, with increasing discharge current yielding a higher peak
temperature.
• The magnitude of the peak temperature along a hollow cathode is dependent upon
the diameter of the cathode, with the peak temperature increasing with decreasing
cathode diameter for a constant flow rate.

Active Zone
• The active zone width increases with decreasing mass flow rates.
• Reducing the flow rate increases the efficiency of the discharge by lowering the
discharge voltage.
44
• The width of the active zone shows a dependence upon the discharge current, with
a doubling of the discharge current increasing the active zone width by
approximately 50%. This increase is brought upon by the additional heating of
the cathode over a larger area which is due to the competing effects of a decreased
sheath voltage with an increased ionization fraction.
• The width of the active zone appears to be controlled by the discharge voltage,
with an increasing voltage resulting in a smaller width.

Location of Peak Temperature
• The location of the peak temperature along the hollow cathode is independent of
discharge current.
• The location of the peak temperature along the hollow cathode is dependent upon
mass flow rate, with higher flow rates moving the peak temperature further down-
stream.
• Location of the peak temperature along the hollow cathode is dependent upon the
diameter of the cathode, with the peak temperature moving further downstream
towards the exit plane with decreasing cathode diameter at constant mass flow
rate.

Comments:
The focus of a significant portion of Downey’s work was to further the understanding of
the processes responsible for achieving the lowest possible cathode material erosion rate.
He demonstrates that a significant reduction in the peak operating temperature can be
45
achieved from a corresponding reduction in discharge voltage. This reduction in
discharge voltage would in turn reduce the gas density in the cathode interior. By
lowering the gas density, the peak cathode temperature would decrease with a
corresponding growth in size of the active zone. A growth in the size of the active zone
would reduce erosion rates at local “hot spots” while correspondingly reducing the
thermal loading on the cathode. As a result, longer cathode operational lifetimes would
be possible.
Another concept furthered by Downey, was that of an alternative means of
reducing the interior gas density of a hollow cathode. He argues that the interior gas
density can be reduced by a lowering of the gas flow rate or a change in the physical
geometry of the cathode itself. By lowering the gas flow rate and altering the cathode
geometry, a lesser amount of gas is able to flow in a larger area, therefore, the peak
cathode temperature is consequently lowered. However, Downey warns that in the case
of MCHC’s, designers must be aware of the increasing demand on discharge power if the
gas density falls too low.
In addition to providing a means for lowering cathode peak operation
temperature, Downey’s work has provided further insight into the cathode arc attachment
phenomena. With the generation of experimental data correlating IPC properties with
cathode operating conditions, and temperature profiles with design and discharge
operating conditions, his research has significantly added to the growing database of
knowledge within the field.

46

Chapter 4: Chapter 4: Chapter 4: Chapter 4:

Role of this Work Role of this Work Role of this Work Role of this Work

The objective of this work is to provide a better understanding of the operating
characteristics (i.e. current, voltage, mass flow rate, cathode material, gas type, etc.)
responsible for affecting solid cathode lifetime. Because cathode lifetimes have been
shown to be strongly linked to temperature, an examination of the cathode axial
temperature distributions combined with measurements of the rates of cathode erosion
are of prime importance. It has been shown that due to a lower surface work function,
thoriated tungsten cathodes operate at significantly lower temperatures than that of pure
tungsten. Due to the large differences in operating temperatures, measurements
comparing erosion rates among both types of cathodes with a comparison between start-
up and steady state operation are of great value.
Electron temperatures, electron densities, and plasma potentials were measured
near the cathode tip (and far plasma for comparison) in order to characterize the plasma
environment in an attempt to verify future model predictions of the near-cathode plasma.
The purpose of the near-cathode plasma model is to help determine the surface heat flux
and current density. These parameters play a large role in dictating cathode surface
47
temperatures, and in turn, the corresponding erosion rates. Listed are some of the
important findings sought throughout the course of this research:

Proposed relationships to be revealed:

• The progression of a time dependent axial temperature profile of a thoriated
tungsten cathode surface and its dependence on an approximated changing
work function.

• A correlation between the location of measured maximum temperature and
the degree of cathode erosion at that location in pure tungsten cathodes with
a comparison to thoriated cathodes.

• A comparison of the erosion rates of both pure and thoriated tungsten
cathodes after various run times.

• Measurements showing that erosion rates are largest during the start-up
phase and tend to lessen during steady state in both pure and thoriated
tungsten cathodes.

• Obtainment of the current density profiles in thoriated tungsten cathodes in
order to examine the effect longer run periods have on the magnitude of the
effective work function.

48

Chapter 5

Research Methodology

This work presents the cathode axial temperature profiles obtained from both optical
pyrometry and CCD camera imaging and a discussion of the voltage and current
characteristics of the arc discharge. Of specific interest are the effects mass flow rate has
on discharge voltage and power. In addition, the electron temperature, plasma potential,
and electron density profiles near the active zone and at a downstream location 8 cm from
the anode (for comparison) with propellant mass flow rates of 450 to 640 sccm and
discharge currents of 20 to 60 A are presented.
The cathodes used in the experiment were both pure and 2 percent thoriated
tungsten cathodes measuring 3.96 mm in diameter and 75 mm in length. Supporting the
cathodes was a strip of high-alumina ceramic bolted to a holder composed entirely of
Glass-Mica ceramic. Six evenly spaced holes measuring roughly 1.5 mm in diameter
supplied consistent argon gas dispersion along the cathode base with mass flow rates
ranging from 400 to 640 sccm. Gas flow rates were managed from a dual regulated tank
and controlled and measured with an Omega flow meter (model # FMA-1619A). The
entire experiment was performed in a 0.52 meter diameter by 0.37 meter long cylindrical
49
vacuum chamber (figure 14) connected to a single roughing pump capable of providing
base pressures in the 10 mTorr range with chamber background pressures reaching as
high as 6.75 Torr during operation at the highest flow rates of 640 sccm. The anode was
a copper tube fitting measuring approximately 76 mm long with an inner diameter of 54
mm and was located 6 millimeters from the cathode tip with its center aligned axially
with the cathode. A coil of copper tubing was brazed to the anode and routed to an
external water supply tap to provide cooling to the anode. A custom made high voltage
supply capable of 0 to 850 volts with a maximum power output of 1.2 kW achieved the
initial gas breakdown, while the arc discharge was maintained with a Lambda ESS (62 A,
160 VDC) power source. Cathode surface temperature measurements were obtained with
a single wavelength Leeds and Northrup disappearing filament optical pyrometer (model
# 8622-C) which was oriented directly perpendicular to the 10 mm thick glass viewport
allowing full observational access to the entire length of the cathode.
Temperature measurements with the optical pyrometer were taken manually at 2
mm intervals starting at the cathode tip and ending upstream near the gas outlet. Plasma
data were acquired by a custom built Langmuir probe consisting of a 0.61 mm diameter
tungsten wire with a length of 8 mm unshielded and exposed to the plasma. The probe
was connected to a Hewlett Packard (model # 6217A) power supply capable of biasing
the probe from -60 to +60 volts. Attached to the chamber and holding the probe was a
fast acting pneumatic linear actuator designed to traverse the entire length from the far
plasma environment to the cathode tip at a speed of approximately 55 cm/s. The high
speed linear actuator is necessary in order to provide the short resonance times required
of the probe in the dense plasma, since exposing the probe to the plasma for longer
50
periods of time would result in thermionic emission of electrons from the surface and
prevent data analysis using assumptions of a non-emitting probe [17]. Probe data was
recorded with a Tektronix 640 A digitizing oscilloscope supporting a sampling rate of up
to 2 gigasamples/s.

Figure 14: Front View of the Vacuum Chamber

Figure 15: Side View of the Initial Anode/Cathode Arrangement
51

Figure 16: A General Schematic of the Experimental Setup
(Anode and Cathode Position Reversed)

Cathode surface images were taken post operation from a scanning electron
microscope at the Center of Electron Microscope and Microanalysis (CEMMA) at USC.
CCD camera temperature profiles and plasma intensity contour images were taken with a
PI-MAX intensified CCD camera. Contour images were modified with a 488 nm argon
line bandpass filter and modeled using Techplot visualization software tools. A side view
of the anode/cathode configuration and a schematic diagram of its arrangement with the
location of Langmuir probe data collection highlighted (near the cathode active zone) is
shown in figures 15 and 16 respectively.

52

Figure 17: Voltage-Current Characteristic of a DC Low Pressure
Electrical Discharge Tube [51]

The voltage/current characteristics during the transition from a glow to arc discharge are
highly non-linear. The main characteristics of the discharge such as the breakdown
voltage, the voltage/current characteristic, and the structure of the discharge depend on
the type of gas used, the pressure, electrode material, and electrode geometry [51].
Figure 17 illustrates a typical voltage and current plot of a glow to arc transition.
The first region, known as a dark discharge, is largely invisible to the eye except
for corona discharges and the breakdown itself. In the early stage of this process, known
as the background ionization stage, ions and electrons migrate to the electrodes from the
applied electric field and produce a weak electric current. Increasing the voltage will
transfer an increasing fraction of these ions and electrons. When the voltage between the
anode and cathode is increased far enough to a certain level, all the available electrons
and ions are carried away, causing the current to saturate.
53
In this saturation region, the current remains constant with increasing voltage.
When the voltage between the electrodes is increased beyond the saturation voltage, the
current begins to rise exponentially. At this point, the electric field is now strong enough
to transfer enough energy to gas electrons to ionize a neutral atom. As the electric field
becomes even stronger, secondary electrons begin to ionize other neutral atoms which
lead to an avalanche of electron and ion production.
This location of exponentially increasing current is known as the Townsend
discharge regime. If the internal resistance of the power supply is below a certain
threshold, the gas will breakdown at a characteristic voltage and move into the normal
glow discharge regime. The breakdown voltage for a given gas and electrode
configuration is dependent on the product of the pressure and distance, p×d, as expressed
in Paschen’s law.
Within the normal glow regime, the voltage is almost independent of the current.
As the current is increased, the fraction of the cathode in contact with the plasma
increases to a maximum in which plasma covers the entire cathode surface. After a
further increase of applied current, the electrodes become sufficiently hot enough to emit
electrons thermionically as they undergo a glow-to-arc transition. Characteristic of a
glow discharge is the high energy electrons with T
e
>> T
i
.
Within the initial arc regime, the discharge voltage begins to decrease with
increasing current, until a point where sufficiently large currents are achieved. Following
this steady drop of voltage, the voltage begins to increase slowly as current is increased.
Since the utilization of an external high voltage starter supply would apply a very
large voltage directly across the current supply source (thus potentially damaging the
54
supply), a blocking diode was placed between the voltage and current sources as seen in
figure 18.

Figure 18: Current Source and High Voltage Supply Decoupled by a Blocking Diode

5.1 Propellant

Historically, a large variety of propellants have been considered for MPD operation.
While the current state of the art where thrust is concerned has been unequivocally
demonstrated to be lithium propellant, argon has been chosen for this work due to its
abundance, affordability, low ionization potential, monotonic structure, and easy
storability. It should also be noted that the relationships and modeling work obtained
from studies using argon propellant can typically be applied to studies using lithium [17].

5.2 Optical Pyrometery

To measure the surface temperature of the cathode a single wavelength Leeds and
Northrup disappearing filament optical pyrometer model #8622-C was oriented directly
55
within the viewing area of the 0.375 in thick glass vacuum chamber viewport, allowing
full observational access of the entire length of the cathode. Temperature measurements
were taken manually at 2 mm intervals starting at the cathode tip and ending upstream
near the gas outlet. Within the pyrometer, a filament of tungsten is superimposed over
the cathode as a red notch filter limits the passing wavelength of the incoming light to
650 nm. The current passing through the filament is varied until its brightness matches
that of the cathode and a measurement of the temperature of the filament is taken from
the pyrometer. Since the cathode is an imperfect blackbody (ε
blackbody
> ε
cathode
), a
correction must be made to determine at what temperature for a given emissivity would
the cathode require in order to be as bright at a wavelength of 650 nm as a blackbody at a
brightness temperature T
b
. Planck’s Distribution law is used equating the brightness of a
“graybody” with an equivalent blackbody to solve for the cathode temperature [17]:











- 1
5
2
1
2
gray b
T k
hc
gray
e
hc
λ
λ
ε π
=










- 1
5
2
1 2
b b
T k
hc
e
hc
λ
λ
π
(5.1)

Solving for the graybody temperature gives:









+








- =
1 1 ln
b
T
effective gray
gray
e
T
α
ε
α
,
b
k
hc
λ
α = (5.2)

Where
effective gray
ε is used in place of
gray
ε to account for losses occurring during the light
56
transmission through the glass view port. It has been shown that for tungsten,
effective gray
ε = (0.37) × (the window transmission factor) [2].
Calibration of the optical pyrometer was conducted by means of a linear
extrapolated temperature predictive technique (shown in figure 19). The temperature of a
tungsten wire held under heat was recorded by use of a type K thermocouple and
compared to the values measured by the optical pyrometer. Since the upper temperature
range of the pyrometer could not be directly tested against the thermocouple values,
linear extrapolation was used to convert direct optical pyrometer temperature
measurements to more accurate values. A comparative method of linear extrapolation
has proven to be effective near the upper limits of traditionally used tungsten filament
lamps [28].
Optical Pyrometer Temperature vs. Measured Temperature
1090
1150
1210
1270
1330
1390
1450
1510
1090 1150 1210 1270 1330 1390 1450 1510
Thermocouple Temperature (K)
Optical Pyrometer Temperature (K)
TC(K)
OP(K)
Linear (TC(K))
Linear (OP(K))

Figure 19: A Comparison of Optical Pyrometer
and Thermocouple Temperature Measurements
57
5.3 Langmuir Probe

A fundamental technique for measuring the properties of plasmas is the use of an
electrostatic probe first developed by Langmuir in 1924. In the experiments the probe
consisted of a thin strip of tungsten wire shielded by a non conductive ceramic tube. The
probe was linked to a voltage supply capable of biasing it at alternative voltages both
positive and negative to the ground, with the maximum bias voltage necessary to cover
the entire spectrum of electron energies to be empirically determined. Attached to the
probe was a fast acting pneumatic linear actuator capable of exposing the probe to the
downstream cathode exit plane plasma environment and retracting it in less than 1 ms.
This rapid cycle was necessary in order to ensure the probe did not reach high enough
temperatures to thermionically emit its own electrons, thus preventing an incorrect
measurement of current density in the case of a positive potential bias.

Figure 20: Circuit Diagram of the Langmuir Probe Setup
V
R

V
bias

R
V
bias

Chamber Plasma
Probe
Tip
58
The bias voltage of the probe was pulsed manually from 0 to 60 volts. Current
measurements were obtained by noting the voltage drop across a current carrying resistor.
The resistor voltage drop and probe bias voltage were then recorded by an oscilloscope
and transferred to a PC for analysis. The process was repeated from 0 volts to -60 thus
allowing a complete profile of the collected current measured over the entire range of
biased voltage. A circuit diagram of the Langmuir probe setup can be seen in figure 20,
where V
bias
represents the applied voltage to the probe and V
R
represents the voltage
measured across the resistor in series with the probe.

5.4 Scanning Electron Microscope (SEM)

The surface microstructure and elemental composition of the cathodes were analyzed
using a scanning electron microscope (SEM) in conjunction with energy-dispersive X-ray
spectroscopy (EDS). Multiple runs varying in length form 0 to 8 hours on thoriated
tungsten cathodes helped reveal typical pathways of thorium migration as well as changes
in surface composition.

5.5 CCD Camera Diagnostics

A PI-Max charged-coupled device (CCD) intensified camera located roughly 380 mm
from the cathode was utilized to measure the two-dimensional temperature field and to
59

Figure 21: A Schematic of the CCD Camera Setup

obtain 488 nm bandpass filtered argon line intensity contours. Included in the CCD array
was a low-noise, high dynamic range readout that could be scanned at a variety of pixel
rates. During operation, data acquired by the camera was routed to a computer for
processing and display. The system configuration and data acquisition software was
controlled via computer using Win/View 32 software. A set of five neutral density filters
with optical densities: 0.4, 0.7, 0.9, 1.3, and 2.0 were used to control image intensity. A
schematic of the CCD camera setup can be seen in figure 21.
Attached to the camera was a 16 mm fixed focal length lens. Due to the limited
focal length of the lens, the entire 512 × 512 pixel display could not be utilized, requiring
that the cathode image be magnified via software at a reduced resolution. However, the
useable pixel grid was sufficiently dense to provide accurate cathode temperature profiles
with an average of over 40 intensity data points along the axis of the cathode. The values
60
recorded were later transferred digitally as DAT files to PC and converted to temperature
measurements.
Temperature measurements were obtained using Planck’s spectral radiance
distribution given by

kT / hc
5
if
2
kT / hc 5
if
2
b
f i
if
e
hc 2
1 e
1 hc 2
L
λ - λ λ
λ
≈
- λ
=
(5.3)

where
λ b
L
is the blackbody radiance, h is Planck’s constant, k is Boltzmann’s constant,
if
λ is the central wavelength, and c is the velocity of light. Once the blackbody radiance,
the cathode emittance, the neutral density filter transmittance, and the measured radiance
were determined, the temperature was calculated using

1
*
0
5
if
2
if
1
L
) T , , ( hc 2
ln
k
hc
T
- λ 















+
τ ϕ θ ε
λ λ
= (5.4)

where ) T , , ( ϕ θ ε is the surface emittance at an angle θ relative to the surface normal and
ϕ from some reference line on the surface,
0
τ is the window transmittance, and
*
L
λ
is
the radiance of the source.
The selected value of spectral surface emissivity can have a large effect on the
scaling of temperature. It has been shown [25] that within a range of 0.2, the calculated
temperature can vary by as much as 300 K for the temperature levels relevant to this
61
study. Reliable values of the spectral emissivity of tungsten can be found in [2]. Due to
the relatively polished surface, a value in the lower range (ε = 0.37) was chosen for both
sets of cathodes as the 2 percent thorium content was not considered to have any adverse
effects. For diffuse emitters, the value of the surface emittance is assumed to be
independent of viewing angles. In total, uncertainties in the transmittance of the neutral
density filters, the surface emittance, and the measurement of the incident radiance are
theorized to be under 2 to 3 percent. However, relatively thin oxide layers can have a
significant impact as it is extremely difficult to adequately quantify the effect of changes
in surface composition will have on total emittance [25]. Also, changing surface
roughness can provide even further overestimates of cathode surface temperature [40].

62

Chapter 6

Experimental Results

The results of the series of experiments measuring axial temperature distributions on both
pure and thoriated solid tungsten cathodes as well as measurements of the near-cathode
plasma properties of interest are presented in this chapter.

6.1 Optical Pyrometer Cathode Surface Temperature Profiles

Several runs were conducted including both high-voltage/low-current glow and arc
discharges and high-current/low-voltage arc discharges. For comparison and due to the
initial difficulty of sustaining a high current arc discharge, a small sample of high-
voltage/low-current data is presented. The data recorded for the low current traces is also
included to illustrate the large scaling of temperature at higher currents.
As can be observed from figure 22, the maximum temperature is dependent upon
either pressure or mass flow rate, with higher pressures or mass flow rates enabling
higher temperatures along the entire cathode. The effects of pressure and mass flow rate
on the location of peak temperature along a cathode in this case (glow discharge) is not
63
0 5 10 15 20 25 30
1000
1050
1100
1150
1200
1250
1300
1350
1400
1450
1500
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position (100 mA discharge)

Pure Tungsten (100 sccm, 0.66 kPa)
Pure Tungsten (100 sccm, 0.8 kPa)
Pure Tungsten (90 sccm, 0.8 kPa)
Pure Tungsten (80 sccm, 0.8 kPa)

Figure 22: Change of Cathode Temperature with Distance in a High
Voltage/Low Current Discharge (Glow Discharge)

0 5 10 15 20 25 30
1200
1250
1300
1350
1400
1450
1500
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position (2 Amp discharge)

Pure Tungsten (300 sccm, 0.45 kPa)
Pure Tungsten (500 sccm, 0.66 kPa)

Figure 23: Axial Temperature Profile of a Cathode in a High Voltage/Low
Current Arc Discharge with Changing Pressure and Mass Flow Rate

64
as dominating as in an arc discharge as the location of peak temperature is consistently at
the cathode tip. In the case of an arc discharge at higher current, as seen in figure 23, the
location of the peak temperature is still located at the tip. A higher pressure or an
increase in mass flow rate (both parameters were changed together complicating the
analysis) may be responsible for a modest increase in overall downstream (toward the tip)
cathode temperature with arc attachment being more focused at that location.
Cathode axial temperature profile measurements at high current recorded by
optical pyrometry agree with the common temperature trends observed in previous
research [27], but with significantly higher temperatures detected closer to the cathode
tip, a peak temperature some short distance upstream of the tip, and a corresponding
decrease in temperature observed towards the base [10].
Long duration tests preformed on thoriated tungsten cathodes showed modest
amounts of temperature variability over time. The variability is probably due to thorium
10 15 20 25 30 35 40 45 50 55 60
2550
2600
2650
2700
2750
2800
2850
2900
Discharge Current (A)
Peak Wall Temperature (K)
Peak Wall Temperature vs. Discharge Current (Thoriated Tungsten)

400 sccm, 0.5 kPa
450 sccm, 0.56 kPa
500 sccm, 0.6 kPa
600 sccm, 0.9 kPa

Figure 24: Dependence of Peak Cathode Temperature on Discharge Current
65
migration altering the local work function on the cathode surface during the initial arc
attachment, as well as arc attachment characteristics associated with the starting pressure
and flow rate. Figure 24 shows that the magnitude of the peak temperature is slightly
dependent on discharge current, with a higher discharge current increasing the magnitude
of the peak temperature. Figure 25 shows the same temperature increasing result that
discharge power has on peak wall temperature. In all cases, the location of the peak
cathode temperature is not located at the tip, but rather a few millimeters upstream. The
range of the displacement of the peak temperature from the cathode tip is largely
dependent on the gas density surrounding the cathode. Increasing the mass flow rate (and
density) will tend to increase the discharge pressure at the cathode, encouraging arc
attachment at the tip with a small pressure gradient supporting more diffuse attachment
located a few millimeters upstream. Therefore, as seen in figures 26 to 29, an increase in
mass flow rate will tend to move peak temperatures further toward the cathode tip.

400 600 800 1000 1200 1400
2600
2650
2700
2750
2800
2850
2900
Discharge Power (W)
Peak Wall Temperature (K)
Discharge Power vs. Peak Wall Temperature (Thoriated Tungsten)

400 sccm, 20-50A, 0.5 kPa
450 sccm, 20-50A, 0.56 kPa
500 sccm, 20-50A, 0.6 kPa
600 sccm, 20-50A, 0.9 kPa

Figure 25: Dependence of Peak Cathode Temperature on Discharge Power
66
0 5 10 15 20 25
1500
2000
2500
3000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Thoriated Tungsten (400 sccm, 0.5 kPa, 20A)
Thoriated Tungsten (400 sccm, 0.5 kPa, 30A)
Thoriated Tungsten (400 sccm, 0.5 kPa, 40A)
Thoriated Tungsten (400 sccm, 0.5 kPa, 50A)
Uncertainty Error

Figure 26: Cathode Axial Temperature Profile with Changing Current at 400 sccm
0 5 10 15 20 25
1500
2000
2500
3000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Thoriated Tungsten (450 sccm, 0.56 kPa, 20A)
Thoriated Tungsten (450 sccm, 0.56 kPa, 30A)
Thoriated Tungsten (450 sccm, 0.56 kPa, 40A)
Thoriated Tungsten (450 sccm, 0.56 kPa, 50A)
Uncertainty Error

Figure 27: Cathode Axial Temperature Profile with Changing Current at 450 sccm
67
0 5 10 15 20 25
1500
2000
2500
3000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Thoriated Tungsten (500 sccm, 0.6 kPa, 20A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 30A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 40A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 50A)
Uncertainty Error

Figure 28: Cathode Axial Temperature Profile with Changing Current at 500 sccm
0 5 10 15 20 25
1500
2000
2500
3000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Thoriated Tungsten (600 sccm, 0.9 kPa, 20A)
Thoriated Tungsten (600 sccm, 0.9 kPa, 30A)
Thoriated Tungsten (600 sccm, 0.9 kPa, 40A)
Thoriated Tungsten (600 sccm, 0.9 kPa, 50A)
Thoriated Tungsten (600 sccm, 0.9 kPa, 60A)
Uncertainty Error

Figure 29: Cathode Axial Temperature Profile with Changing Current at 600 sccm
68
Less obvious is the effect of mass flow rate on maximum temperature. From the data
recorded, a decrease in mass flow rate may tend to slightly decrease the magnitude of the
maximum temperature by more evenly distributing the thermal loads across the cathode.
Such change in mass flow would increase the width of the active zone all while
maintaining the same discharge current, thus decreasing the peak thermal loading on the
cathode and reducing the material erosion rate.
Axial temperature error was calculated from averaging the recorded temperature
from two separate sweeps. The largest discrepancy between the average and any single
measured data point determined the range of error (both positive and negative) for the
entire data set.

6.2 Langmuir Probe Data

Langmuir probing was used to obtain measurements for the electron temperature,
electron density, and plasma potential 1 cm axially from the centerline of the cathode tip
(near the active zone) and at a location 8 cm from the midpoint of the back end of the
anode (far plasma). The probe has been modeled as being an infinitely long cylinder and
a nearly perfect absorber of all charged particles reaching its surface. In addition, it is
assumed that the velocities of the electrons and ions at the boundary of the bulk plasma
and probe sheath can be accurately represented as Maxwellian distributed [17]. Because
the probe sheath thickness is on the order of several Debye lengths and is much less than
a mean free path, the sheath region was considered collisionless. Also, in both regions,
the plasma density is sufficiently high with the probe radius being significantly larger
69
than the sheath thickness allowing for a “thin-sheath” analysis [17, 31] with electron
density given by:

e B
s
sat
e
T k
M
2
1
exp qA
I
n






- =
(6.1)

where I
sat
is the ion saturation current, q is the electron charge, A
s
is the collection area of
the probe (or the area representing the probe sheath), M is the ion mass (6.62 · 10
-26
kg
for argon), k
B
is Boltzman’s constant, and T
e
is the electron temperature. The validity of
the probe theory was checked periodically by calculating the ratio of the probe radius to
the Debye length with a ratio typically on the order of 10
3
.

Natural Log of Current vs. Probe Bias Voltage
-10
-9
-8
-7
-6
-5
-4
-3
-2
-70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60
Bias Voltage (V)
Current [ln (A)]
ln(Iprobe-Isat)
Electron Saturation
Electron Transition
Plasma Potential

Figure 30a: Sample Langmuir Probe Trace (Near Cathode Plasma)

70
Natural Log of Current vs. Probe Bias Voltage (Far Plasma)
-5
-4
-3
-2
-1
0
1
2
10 15 20 25 30 35 40 45 50 55
Bias Voltage (V)
Current [(ln (A)]
ln(Iprobe -Isat)
Electron Saturation
Electron Transition
Plasma Potential

Figure 30b: Sample Langmuir Probe Trace (Far Cathode Plasma)

Due to the series of before mentioned approximations, Langmuir probe data should be
regarded as showing largely qualitative trends. Figures 30a and 30b show early
Langmuir Probe I-V curves for both the near cathode tip and far plasma regions. A range
of error due to the uncertainty in the slope of the electron saturation in the far plasma is
reflected on the following plots, however, the near plasma environment showed more
consistent saturation, and therefore, had less uncertainty due to this parameter. Electron
temperatures and electron densities were measured near the cathode tip in order to
characterize the plasma environment in an attempt to verify future model predictions.
Another motivating factor dictating electron density measurements is that electron
density has proven to affect current density at the cathode surface and can be regarded as
a critical sheath boundary parameter [25]. In addition, because of the interdependent
71
nature of near-cathode plasma models and thermal plasma models, electron temperature
measurements are necessary in cataloging the energy flux within the ionization region.
Such energy transport is largely dependent on temperature (and by association thermionic
emission). As the thermionic current increases, more energy is added to the ionization
region and the electron temperature increases. The total heat flux at the cathode is
initially positive and becomes negative due to the cooling effect of thermionic electrons
as they begin to dominate the heating effects for the ions and the plasma electrons [25].
Within the arc plasma environment, the energy required for the ionization of
neutral atoms is mostly supplied by a series of inelastic collisions with electrons resulting
in ionization dominated by stepwise excitation. These collisions result from the transfer
of energy from the kinetic impacts of the colliding electrons and argon neutral particles.
Such impacts lead to a relocation of internal energy to the electron charge carriers.
30 35 40 45 50 55 60 65
0
1
2
3
4
5
6
Discharge Currrent (A)
Electron Temperature (eV)
Electron Temperature vs. Discharge Current (Thoriated Tungsten)

640 sccm
600 sccm
550 sccm
500 sccm
450 sccm
640 sccm (Far Plasma)
600 sccm (Far Plasma)
550 sccm (Far Plasma)
500 sccm (Far Plasma)
450 sccm (Far Plasma)
Uncertainty Error

Figure 31: Electron Temperature vs. Discharge Current
72
Figures 31 and 32 show the dependence of the electron temperature on discharge
current and mass flow rate (with pressures ranging from 0.5-0.9 kPa depending on mass
flow rate). From the plots it is apparent that for the far plasma environment downstream
of the anode, electron temperatures are considerably higher as compared to the near
cathode values, and therefore, there is a higher probability of any given electron yielding
an ionization event. However, because the electron densities are significantly lower,
collisions between electrons and neutral atoms are substantially reduced, thus available
energy from the electrons is not transferred nearly as readily as in the case of the active
zone electrons. The ratio of the electron temperature to the ion temperature (T
e
/T
i
) near
the sheath region is largely unknown. However, for the high pressure arcs of these
experiments, approximating T
e
= T
i
has shown to correlate well with model predictions,
yielding electron temperatures in the 0.5 – 0.7 eV range [25].
400 450 500 550 600 650
0
1
2
3
4
5
6
Mass Flow Rate (sccm)
Electron Temperature(eV)
Electron Temperature vs. Mass Flow Rate (Thoriated Tungsten)

35 A
40 A
45 A
50 A
55 A
60 A
40A (Far Plasma)
45A (Far Plasma)
50A (Far Plasma)
55A (Far Plasma)
60A (Far Plasma)
Uncertainty Error

Figure 32: Electron Temperature vs. Mass Flow Rate
73
30 35 40 45 50 55 60 65
0
2E+12
4E+12
6E+12
8E+12
1E+13
1.2E+13
1.4E+13
1.6E+13
1.8E+13
2E+13
Discharge Currrent (A)
Electron Density (#/cm
3
)
Electron Density vs. Discharge Current (Thoriated Tungsten)

640 sccm
600 sccm
550 sccm
500 sccm
450 sccm
640 sccm (Far Plasma)
600 sccm (Far Plasma)
550 sccm (Far Plasma)
500 sccm (Far Plasma)
450 sccm (Far Plasma)
Uncertainty Error

Figure 33: Electron Density vs. Discharge Current

A general increase in electron temperature (up to 6 eV) with axial distance from
the cathode has been observed in previous research on lower current hollow cathodes
[31]. Higher electron temperatures in the far plasma region are likely due to a transition
from the near plasma arc dominated high current density regime to a lower current
density glow-like regime. Because of the high electron densities and low electron
temperatures near the cathode tip, ionization is largely maintained by a stepwise process.
However, the low current density far plasma environment necessitates that the ionization
is sustained mainly by high temperature direct electron impact.
Increasing the discharge current or mass flow rate has the effect of reducing
electron temperature, a trend witnessed in similar experimental studies [17, 18].
Increasing the mass flow rate will reduce electron temperatures because adding more
74
400 450 500 550 600 650
2E+12
4E+12
6E+12
8E+12
1 E+13
1.2E+13
1.4E+13
1.6E+13
1.8E+13
2E+13
Mass Flow Rate (sccm)
Electron Density (#/cm
3
)
Electron Density vs. Mass Flow Rate (Thoriated Tungsten)

35 A
40 A
45 A
50 A
55 A
60 A
40A (Far Plasma)
45A (Far Plasma)
50A (Far Plasma)
55A (Far Plasma)
60A (Far Plasma)
Uncertainty Error

Figure 34: Electron Density vs. Mass Flow Rate

neutrals will increase the electron to neutral collision frequency, thereby ensuring that
more energy is expended not on electron ionization but rather on exciting more neutral
atoms. As can be seen from Figures 33 and 34, the electron density is a slightly
increasing function of both discharge current and mass flow rate. As expected, the
numbers of near cathode electrons are substantially higher than in the far plasma case.
From figure 35, it appears that at all currents levels and mass flow rates, the near
cathode plasma potential (1 cm from the cathode tip) is relatively constant with
increasing discharge current. Such a relationship was witnessed on a similar Langmuir
probe study [17] in which the plasma potential was shown to be nearly constant with
increasing discharge current at higher mass flow rates. However, it was shown in the
study that for the lower mass flow rates tested, the potential was clearly a decreasing
75
function of discharge current. Because this work focused only on Langmuir probe
studies at even higher mass flow rates, a similar dependence in the near cathode plasma
environment was not witnessed. An evaluation of the data recorded has shown that no
clear reliable dependence of plasma potential on discharge current can be concluded in
the near-cathode tip plasma environment.
The trend of the data for the far plasma demonstrates a continual decrease in
plasma potential with increasing current, with potentials roughly over an order of
magnitude higher than near the cathode tip. Figure 36 shows that near the cathode tip
and in the far plasma case, generally, the cathode potential decreases slightly with an
increase in mass flow rate. However, this is not the case over all current levels tested.
As expected the plasma potential measurements are significantly higher within the far
plasma regime than near the cathode tip.

30 35 40 45 50 55 60 65
0.2
0.4
0.6
0.8
1
2
4
6
8
10
20
30
40
50
Discharge Currrent (A)
Plasma Potential (V)
Plasma Potential vs. Discharge Current (Thoriated Tungsten)

640 sccm
600 sccm
550 sccm
500 sccm
450 sccm
640 sccm (Far Plasma)
600 sccm (Far Plasma)
550 sccm (Far Plasma)
500 sccm (Far Plasma)
450 sccm (Far Plasma)
Figure 35: Plasma Potential vs. Discharge Current
76
400 450 500 550 600 650
0.2
0.4
0.6
0.8
1
2
4
6
8
10
20
30
40
50
Mass Flow Rate (sccm)
Plasma Potential(V)
Plasma Potential vs. Mass Flow Rate (Thoriated Tungsten)

35 A
40 A
45 A
50 A
55 A
60 A
40A (Far Plasma)
45A (Far Plasma)
50A (Far Plasma)
55A (Far Plasma)
60A (Far Plasma)
Figure 36: Plasma Potential vs. Mass Flow Rate

6.3 Discharge Current/Voltage Characteristics

Several runs of the 3.96 mm diameter thoriated tungsten cathodes with currents between
20-60 A, mass flow rates from 450-640 sccm, and pressures between 0.5-0.98 kPa
demonstrated typical current/voltage relationships in a plasma-diffuse arc discharge. As
seen in figures 37 and 38, for lower mass flow rates, the discharge voltage drops steadily
as current is increased. This relation is also observed at higher mass flow rates,
however, the rate of voltage drop with the increasing current is reduced and instead the
voltage begins to increase slightly with increasing current. Such a trend can be partially
explained by Paschen’s law, which describes the breakdown voltage of a gas as a
77
function of pressure and gap distance between electrodes. In the initial gas breakdown of
an arc discharge or its re-ignition [12], more collisions between electrons and gas
molecules will take place as the pressure-gap product is increased. Since the occurrence
of more collisions increases the randomization of the electron trajectories, the electrons
are no longer solely being accelerated by the electric field and can actually be decelerated
as they frequently travel back towards the cathode. Because electron energy is reduced,
larger voltages are necessary to assure ionization of enough gas molecules to initiate the
discharge. Although the strict application of Paschen’s law does not hold true for an
already established arc, a close variant is likely responsible for the slight increase of
voltage at higher pressure. Both figure 39 and figure 40 show similar trends while
illustrating the effect mass flow rate has on discharge resistance and power, with figure
41 showing the effect plasma resistance has on discharge current.
10 20 30 40 50 60 70
18
20
22
24
26
28
30
Discharge Current (A)
Discharge Voltage (V)
Discharge Voltage vs. Discharge Current (Thoriated Tungsten)

450 sccm, 0.56 kPa
500 sccm, 0.6 kPa
550 sccm, 0.72 kPa
600 sccm, 0.9 kPa
640 sccm, 0.98 kPa

Figure 37: Discharge Voltage vs. Discharge Current
78
400 450 500 550 600 650
18
20
22
24
26
28
30
Mass Flow Rate (sccm)
Discharge Voltage (V)
Discharge Voltage vs. Mass Flow Rate (Thoriated Tungsten)

20A
30A
40A
50A
60A
Figure 38: Discharge Voltage vs. Mass Flow Rate

400 450 500 550 600 650
0.9
1
1.1
1.2
1.3
1.4
1.5
Mass Flow Rate (sccm)
Resistance(ohms)
Discharge Resistance vs. Mass Flow Rate (Thoriated Tungsten)

20A
30A
40A
50A
60A

Figure 39: Discharge Resistance vs. Mass Flow Rate

79
As can be seen from figure 41, the discharge resistance is a decreasing function of the
discharge current. The lowering of the resistance with increasing current is a well-known
negative differential resistance phenomenon seen in arc discharges.
Initially at start-up, the gas is composed of neutral atoms with high resistance.
After initial breakdown of the gas, the high voltage applied to the particles accelerates the
particles, necessitating a large increase in kinetic energy. The high energy electron and
ion pairs continue to collide with other particles and free more electrons and ions. After a
substantial number of neutrals have been ionized, the plasma resistance begins to drop
due to the high number of free charge carriers. In order to maintain a stable discharge,
the power source is required to compensate by increasing its voltage output. The entire

400 450 500 550 600 650
400
500
600
700
800
900
1000
1100
1200
1300
1400
Mass Flow Rate (sccm)
Discharge Power (W)
Discharge Power vs. Mass Flow Rate (Thoriated Tungsten)

20A
30A
40A
50A
60A

Figure 40: Discharge Power vs. Mass Flow Rate

80
10 20 30 40 50 60 70
0.9
1
1.1
1.2
1.3
1.4
1.5
Discharge Current (A)
Resistance (ohms)
Discharge Resistance vs. Discharge Current (Thoriated Tungsten)

450 sccm, 0.56 kPa
500 sccm, 0.6 kPa
550 sccm, 0.72 kPa
600 sccm, 0.9 kPa
640 sccm, 0.98 kPa

Figure 41: Discharge Resistance vs. Discharge Current

process stops if the power source is unable to supply enough voltage. In such a scenario,
the arc either reaches steady state or is extinguished. As with start-up, an added
abundance of charge carriers in steady state operation ensures a drop in the discharge
resistance.

6.4 Cathode Surface Topography and Composition

In this study four individual cathodes were examined under a scanning electron
microscope (SEM) with their elemental composition analyzed by energy-dispersive X-
ray spectroscopy (EDS). A magnified unused thoriated tungsten cathode is compared to
cathodes with run times varying from 2 to 8 hours of operation. After 2 hours, the
surface microstructure was dominated by severe cratering characteristic of the start-up
phase of the discharge. As predicted, lying within many of the craters are large deposits
81
of thorium metal. The destructive cratering process has been theorized to excavate
deposits of thorium from the cathode bulk [25]. Figures 42(A) – 42(L) show the
progression of this phenomenon.
Figure 42(A) shows the relatively smooth, yet lightly scathed surface of an
unused thoriated tungsten cathode. Much of this noticeable surface roughness can be
attributed to the initial metallurgical processes in which thorium enriched tungsten
powder is compressed under high pressure and temperature to produce solid rods.
Generally, the thorium oxide additives are dispersed finely in the tungsten prior to
forming and cathodes show no evident signs of thorium metal on the surface.
Figures 42(B) through 42(D) show major changes in surface structure after 2
hours. As discussed in section 2.1, the cathode surface was dominated by a significant
number of craters with deposits of thorium lying within. As mentioned, a significant
number of these craters develop within the start-up phase of the discharge and can be
observed in a matter of seconds [25]. Characteristic of this shorter run time is the lower
occurrence of craters with thorium deposits. However, the craters accompanying the
largest deposits did not appear to be dependent on run time, as the cathode operated for 2
hours had the largest single deposit of thorium with a maximum length of nearly 100 µm.
After 4.5 hours (figure 42(E) to 42(G)) of operation, there is a significant increase
in the amount of craters with thorium deposits. Much of the noticeable increase is
evident at the cathode tip and can be considered not to be a product of the initial start-up
phase (since much of the arc attachment happens closer to the cathode base), but rather a
consequence of continuous steady attachment at that location. The maximum size of any
single deposit was smaller in this case, with the largest reaching approximately 40 µm in
82

Figure 42(A): The Surface of an Unused Figure 42(B): A Thoriated Tungsten
Thoriated Tungsten Cathode at Cathode (Upstream of Tip) After
250× Magnification 2 Hours at 250× Magnification

Figure 42(C): A Thoriated Tungsten Figure 42(D): A Thoriated Tungsten
Cathode (Near the Tip) After 2 Cathode (Near the Tip) After 2
Hours at 250× Magnification Hours at 650× Magnification
83

Figure 42(E): A Thoriated Tungsten Figure 42(F): A Thoriated Tungsten
Cathode (at the Tip) After 4.5 Hours Cathode (at the Tip) After 4.5 Hours
at 160× Magnification at 650× Magnification

Figure 42(G): A Thoriated Tungsten Figure 42(H): A Thoriated Tungsten
Cathode (at the Tip) After 4.5 Hours Cathode After 8 Hours
at 1500× Magnification at 35× Magnification
84

Figure 42(I): A Thoriated Tungsten Figure 42(J): A Thoriated Tungsten
Cathode After 8 Hours Cathode After 8 Hours
at 85× Magnification at 450× Magnification

Figure 42(K): A Thoriated Tungsten Figure 42(L): A Thoriated Tungsten
Cathode After 8 Hours Cathode After 8 Hours
at 600× Magnification at 850× Magnification

85
length. Longer continuous run times should prove to limit the maximum size of any
single deposit, however, more tests will need to be conducted to demonstrate such a
relationship.
Figures 42(H) through 42(L) show a cathode tip after operating for 8 hours. As
observed, there is a significant accumulation and redistribution of tungsten crystals. It
has been proposed that these areas of tungsten crystal accumulation are formed by
recrystallization of tungsten at high operating temperatures or by the vapor deposition of
tungsten [25]. It should be noted that [25] also noted an enormous concentration of
thorium metal at the surface tip with significant restructuring accompanied by structures
that looked like fern leaves. Such transformation and restructuring near the tip was not
observed in the course of this study, however, the cathodes utilized were ran at
considerably lower currents and for significantly shorter periods of time. It has been
theorized that the evaporated thorium vapor is ionized outside the sheath and drawn back
to the surface by the electric field. It is this process that may provide the means for the
redistribution of thorium from the bulk to the tip. The lower electric fields characteristic
of this study may explain why no such occurrence was observed.
Figures 43-46 show the energy-dispersive X-ray spectrum (EDS) used to
identify the major elemental constituents of the four cathodes. A sizeable increase of
both carbon and oxygen were observed on the cathodes with longer runtimes and may
have been a product of minor leaks and component outgassing in the vacuum facility.
Such leaks are undesirable as increased oxygen levels can increase the mass loss rate of
tungsten (see section 2.7). No clear trend was identified relating the percent composition
change of thorium and tungsten over time. The absence of such a relation may be due to
86
an appreciably low total evaporation mass of cathode material after the maximum 8 hour
run time. Further tests with longer runtimes would need to be conducted in order to
determine how thorium evaporation rates compare with that of tungsten. However, such
post test analysis can be a challenge due to the possible tendency of thorium to be
transferred and deposited back to the surface. It should be noted that the EDS spectrum
in figure 44 reveals lower values of both carbon and oxygen, as well as no traces of
thorium. Such an absence is unwarranted and is expected to be the result of EDS
measurement error. As a result, the data in figure 44 should not be considered reliable.

Figure 43: EDS Spectrum of an Unused Thoriated Tungsten Cathode

87

Figure 44: EDS Spectrum of a Thoriated Tungsten Cathode After 2 Hours

Figure 45: EDS Spectrum of a Thoriated Tungsten Cathode After 4.5 Hours
88

Figure 46: EDS Spectrum of a Thoriated Tungsten Cathode After 8 Hours

6.5 Charged-Coupled Device (CCD) Camera Temperature Profiles

Both current and time dependent (2-8 hours) thoriated tungsten temperature profiles
were recorded using CCD camera imaging. The general trends in the profiles largely
matched those obtained via optical pyrometry, with higher temperatures measured at
the cathode tip, a peak temperature at roughly 4 to 7 mm upstream, and a corresponding
decrease in temperature towards the base. Peak temperatures of roughly between 2600
and 2800 K at a location near the tip of the cathode were routinely recorded, along with
minimum temperatures of between 2100-2400 K at a distance of approximately 18 mm
from the tip. Figure 47 shows a sample intensity profile of a thoriated tungsten
cathode.
89

Figure 47: A 2D Image of the Measured Intensity Distribution
of a Thoriated Tungsten Cathode at 60 A and a Mass Flow
Rate of 640 sccm Represented by Pseudo Colors

0 2 4 6 8 10 12 14 16 18
1500
2000
2500
3000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Thoriated Tungsten (500 sccm, 0.6 kPa, 30A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 40A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 50A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 60A)

Figure 48: Cathode Axial Temperature Profile After 2 Hours
90
0 2 4 6 8 10 12 14 16 18
1500
2000
2500
3000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Thoriated Tungsten (500 sccm, 0.6 kPa, 30A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 40A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 50A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 60A)

Figure 49: Cathode Axial Temperature Profile After 4 Hours

0 2 4 6 8 10 12 14 16 18
1500
2000
2500
3000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Thoriated Tungsten (500 sccm, 0.6 kPa, 30A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 40A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 50A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 60A)

Figure 50: Cathode Axial Temperature Profile After 6 Hours

91
0 2 4 6 8 10 12 14 16 18
1500
2000
2500
3000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Thoriated Tungsten (500 sccm, 0.6 kPa, 30A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 40A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 50A)
Thoriated Tungsten (500 sccm, 0.6 kPa, 60A)

Figure 51: Cathode Axial Temperature Profile After 8 Hours

As shown in figures 48-51, and with the studies using optical pyrometry, the peak
surface temperature is an increasing function of discharge current. Such a trend was
observed over all the time periods tested. A progressive flattening of the temperature
profiles with time was observed. For example in the first case of a 60 A discharge
operating for two hours, a maximum surface temperature of approximately 2825 K was
observed with a corresponding minimum temperature of about 2300 K. However, for
the same current level and after 6 hours, a maximum and minimum temperature of
about 2625 K and 2230 K respectively, were recorded. Therefore, the surface
temperature gradient along the bulk cathode was largely reduced during the longer run
time. This trend was repeatedly observed over all current levels.
Any model attempting to predict the operational lifetime of a thoriated tungsten
cathode will need to catalog surface heat fluxes and current densities near the cathode
92
tip. Because cathode current profiles are necessarily dependent on temperature (which
is affected by the cathode plasma attachment characteristics), a proper analysis of
cathode tip arc attachment phenomena is crucial. Figures 52 and 53 show 488 nm
bandpass filtered argon line intensity contours at the cathode tip at 60 A after 2 and 8
hours respectively. Together these contour images illustrate the large axial intensity
gradient over a short distance. As expected, the highest intensity levels are located very
near and surrounding the tip. It should be noted that the plasma intensity distribution
tended to become slightly more diffuse with time. However, because the intensity
contours do not show drastic variability, it is unclear if this is a real time dependent
phenomena or simply standard fluctuations.

Figure 52: 488 nm Bandpass Filtered Argon Line Intensity Contours for a
Tungsten Cathode Tip After 2 Hours at 60 A and a Mass Flow Rate of 500 sccm

93

Figure 53: 488 nm Bandpass Filtered Argon Line Intensity Contours for a
Tungsten Cathode Tip After 8 Hours at 60 A and a Mass Flow Rate of 500 sccm

0 2 4 6 8 10 12 14 16 18
1500
2000
2500
3000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Thoriated Tungsten (500 sccm, 0.6 kPa, 2 hr)
Thoriated Tungsten (500 sccm, 0.6 kPa, 4 hr)
Thoriated Tungsten (500 sccm, 0.6 kPa, 6 hr)
Thoriated Tungsten (500 sccm, 0.6 kPa, 8 hr)

Figure 54: Cathode Axial Temperature Profile at 30 Amps

94
0 2 4 6 8 10 12 14 16 18
1500
2000
2500
3000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Thoriated Tungsten (500 sccm, 0.6 kPa, 2 hr)
Thoriated Tungsten (500 sccm, 0.6 kPa, 4 hr)
Thoriated Tungsten (500 sccm, 0.6 kPa, 6 hr)
Thoriated Tungsten (500 sccm, 0.6 kPa, 8 hr)

Figure 55: Cathode Axial Temperature Profile at 40 Amps

0 2 4 6 8 10 12 14 16 18
1500
2000
2500
3000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Thoriated Tungsten (500 sccm, 0.6 kPa, 2 hr)
Thoriated Tungsten (500 sccm, 0.6 kPa, 4 hr)
Thoriated Tungsten (500 sccm, 0.6 kPa, 6 hr)
Thoriated Tungsten (500 sccm, 0.6 kPa, 8 hr)

Figure 56: Cathode Axial Temperature Profile at 50 Amps

95
0 2 4 6 8 10 12 14 16 18
1500
2000
2500
3000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Thoriated Tungsten (500 sccm, 0.6 kPa, 2 hr)
Thoriated Tungsten (500 sccm, 0.6 kPa, 4 hr)
Thoriated Tungsten (500 sccm, 0.6 kPa, 6 hr)
Thoriated Tungsten (500 sccm, 0.6 kPa, 8 hr)

Figure 57: Cathode Axial Temperature Profile at 60 Amps

Figure 58: Cathode Peak Wall Temperature vs. Time
96

Figure 59: Cathode Wall Temperature vs. Time at Various Locations at 640 sccm

Figures 54-57 show the change in surface temperature with time for varying
current levels. For lower currents such as 30 A, the temperature values did not change
with time as readily as with higher currents. As seen in figure 58, there was only slightly
over a hundred degree Kelvin difference in peak temperature between the 2 hr and 8 hr
run times. However, at 60 A there is approximately a two hundred degree Kelvin
difference in peak temperature during the same run period. Also, it should be noted that
the location of peak temperature tends to shift 1-2 mm upstream of the cathode after
longer cathode burn periods. The degree of variability in the location of peak
temperature as it changes with time does not appear to be dependent on current.
Some caution must be exercised when examining the magnitude of the time-
dependant change of cathode surface temperatures. Such dependence was shown to
97
fluctuate between alternate runs, and in some cases, the temperature along the cathode tip
was shown to slightly increase during the time periods relevant to this study. A
comparison of figures 58 and 59 show the uncertainty in the time dependent temperature
profiles between two runs, as the range of temperature drop was only slightly over one
hundred degrees Kelvin near the tip during the 8 hour run period shown in figure 59. In
addition, time dependent tests on pure tungsten cathodes demonstrated the potential
cooling capability (up to 500 K) of cathode material near the tip given a constant work
function. Time dependent fluctuations in the arc attachment profile are theorized to be
the cause of such redistribution of temperature along the surface. However, it should be
noted that thoriated tungsten cathodes routinely demonstrated a significantly more
consistent arc attachment profile. In the case of thoriated cathodes, there is difficulty
determining how much of the temperature variation is due to the changing thorium
surface coverage or slight variations in the arc attachment along the surface.
0 2 4 6 8 10 12 14 16 18
1500
2000
2500
3000
3500
4000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Pure Tungsten (500 sccm, 0.6 kPa, 60A)
Pure Tungsten (500 sccm, 0.6 kPa, 50A)
Pure Tungsten (500 sccm, 0.6 kPa, 40A)
Pure Tungsten (500 sccm, 0.6 kPa, 30A)

Figure 60: Pure Tungsten Cathode Axial Temperature Profile at 500 sccm
98

0 2 4 6 8 10 12 14 16 18
1500
2000
2500
3000
3500
4000
Distance from Cathode Tip (mm)
Cathode Material Temperature (K)
Cathode Material Temperature vs. Position

Pure Tungsten (640 sccm, 0.95 kPa, 60A)
Pure Tungsten (640 sccm, 0.95 kPa, 50A)
Pure Tungsten (640 sccm, 0.95 kPa, 40A)

Figure 61: Pure Tungsten Cathode Axial Temperature Profile at 640 sccm

Figure 62: Pure and Thoriated Tungsten Cathodes with Notable Erosion at the
Location of Maximum Temperature on the Pure Tungsten Cathode After 4 Hours

0 mm
Pure tungsten
after 10.5 hours
Thoriated
tungsten after 16
hours
maximum
temperature
10 mm
Pure tungsten
after 4 hours
99

Figure 63: Cathode Material Evaporative Mass Loss vs. Time at 60 A

Figure 64: Pure Tungsten Cathode Radius vs. Distance From the Initial Tip
100
The lower operating temperatures in thoriated tungsten cathodes significantly
reduce the erosion rate making them a more practical electrode material for thrusters [49].
However, the distribution of thorium along the surface can drastically alter the local work
function, the discharge characteristics, and in turn the axial temperature profiles. The
rapid depletion of thorium is to be expected in electric thruster cathodes after long burn
times [53]. In these studies, the shorter run times ensured that a sufficient supply of
thorium was able to diffuse from the cathode interior at a rate which was largely higher
than losses due to both evaporation and migrational transport to the surrounding plasma.
Figures 60 and 61 show the temperature profiles for a pure tungsten cathode with
varying current. As expected the maximum temperatures near the tip are significantly

0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 5 10 15 20 25
Distance From Cathode Tip (mm)
Thermionic Electron Emission (A/cm
2
)
ϕ = 4.5 eV
3.5 eV
3.4 eV
3.3 eV
3.2 eV
3.1 eV
3.0 eV
2.9 eV
2.8 eV

Figure 65: Thermionic Electron Emission Current Density vs. Distance
From the Cathode Tip at 60 A, 600 sccm, and 0.9 kPa for Possible Ranges of Work
Function for Thoriated Tungsten Cathodes
101
higher than in the case of thoriated tungsten and approach the melting point of the metal.
The profiles show the dominating effect work function has on surface temperature for the
difference between 4.55 eV for tungsten [7] and 2.6 – 4.0 eV for 2 percent thoriated
tungsten [25].
Figure 62 shows the severe surface erosion of two pure tungsten cathodes after
being exposed to a discharge for 4 and 10.5 hours. Noticeable erosion at the tip can be
seen in both cases. The 4 hour case demonstrated the largest single area of erosion at a
location approximately 3 mm upstream of the cathode near the region of maximum
temperature. The thoriated tungsten cathode, however, showed significantly less mass
loss (an actual gain) after being exposed for 16 hours. Figure 63 shows the measured

Figure 66: Temperature vs. Thermionic Current
Density for 2.8 < φ φ φ φ < 4.5 eV
102
mass loss for both types of cathodes after being exposed to a discharge for at least 10.5
hours. An initial mass loss of approximately 6 mg of cathode material was measured by
use of an analytic scale from the thoriated cathode after being exposed to the discharge
for only 10 minutes. The initial mass loss proved to be the cathode’s upper limit as it
actually gained some small amount of mass after running for close to 16 hours. The
increase in mass is likely due to cathode holder or anode material being re-deposited on
the cathode. Because the initial start-up phase tends to encourage attachment near the
base where the cathode is being held, a small but significant amount of holder material
may be vaporized and exposed to the cathode. In addition, the copper anode which is in
very close proximity to the cathode tends to erode itself and some material may also
reach the cathode. These results have shown that the start-up phase is significantly more
damaging to thoriated tungsten cathodes in these conditions as little mass is lost when
running in steady state mode. The pure tungsten cathodes exhibited the largest degree of
mass loss during start-up. However, unlike the thoriated tungsten cathodes, they showed
more consistent mass loss with longer run times. The initial and final shape of a pure
tungsten cathode after 10.5 hours can be seen in figure 64.
Both Figures 65 and 66 show thermionic current densities for a large portion of
the range of possible work function values in thoriated tungsten cathodes. The lowering
of temperature with work function for a given current density is illustrated in figure 66.
Current density values were obtained from the Richardson-Dushman equation given in
section 2.3 with constant A
R
values of 60 A/cm
2
/K
2
for pure tungsten and 120 A/cm
2
/K
2

for thoriated tungsten. Although the Richardson coefficient changes with temperature, it
was assumed to be constant in order to simplify the analysis. Also, the magnitude of the
103
electric field at the cathode surface is primarily determined by the characteristics of the
sheath region. The Schottky effect can influence and change the thermionic emission
current density and reduce the local work function by several tenths of an electron volt.
Due to the inherent difficulties of calculating the Scottky effect, its influence was
ignored. As a result, the above graphs show largely approximate trends.
Figures 67(A) – 67(D) show calculated current density profiles from the thoriated
tungsten temperature profiles obtained using the CCD camera. A polynomial fit of the
curves was applied to obtain an analytical solution that could be integrated in sections.
The values for the effective work function were determined by integrating these current
density profiles over the entire cathode length and equating those values to the total
current being driven by the power supply. Once those values were in agreement, a value
for the effective work function could be obtained from the Richardson-Dushman
equation.
The profiles show a slight yet consistent reduction in work function over the 8
hour run period. Because cathode surface temperatures were shown to lower on average
with time, the attachment area would necessarily need to increase. Such an increase may
necessitate the need for larger cathodes.
From the profiles, the length of active zone (the area responsible for 70% of the
emitted thermionic current) was calculated to be between 7 to 8 mm. Along the cathode,
the attachment area was shown to increase with time while current densities exhibited a
slight decrease. Table 3 shows the changing values for the average attachment area and
current density for 70%, 80%, and 90% of the emitted current from the cathode.

104

Figure 67(A): Thermionic Current Figure 67(B): Thermionic Current
Density vs. Distance From the Density vs. Distance From the
Cathode Tip at 60A after 2 hours Cathode Tip at 60A after 4 hours

Figure 67(C): Thermionic Current Figure 67(D): Thermionic Current
Density vs. Distance From the Density vs. Distance From the
Cathode Tip at 60A after 6 hours Cathode Tip at 60A after 8 hours

105

Time (hr),
I = 70%
P = 0.6 kPa
I
tot
(A) A
attach
(mm
2
) j (A/mm
2
) Length (mm) Φ
eff
(eV)
2 60 A 176.66 0.238 7.1 3.36
4
6
8
60 A
60 A
60 A
181.63
189.10
194.08
0.231
0.222
0.216
7.3
7.6
7.8
3.25
3.10
3.08

Time (hr),
I = 80%
P = 0.6 kPa
I
tot
(A) A
attach
(mm
2
) j (A/mm
2
) Length (mm) Φ
eff
(eV)
2 60 A 211.49 0.227 8.5 3.36
4
6
8
60 A
60 A
60 A
213.98
218.96
221.44
0.224
0.219
0.217
8.6
8.8
8.9
3.25
3.1
3.08

Time (hr),
I = 90%
P = 0.6 kPa
I
tot
(A) A
attach
(mm
2
) j (A/mm
2
) Length (mm) Φ
eff
(eV)
2 60 A 263.74 0.205 10.6 3.36
4
6
8
60 A
60 A
60 A
268.72
273.70
278.68
0.201
0.197
0.194
10.8
11
11.2
3.25
3.1
3.08

Table 3: Experimental Data for a Thoriated Tungsten Cathode at 0.6 kPa Table 3: Experimental Data for a Thoriated Tungsten Cathode at 0.6 kPa Table 3: Experimental Data for a Thoriated Tungsten Cathode at 0.6 kPa Table 3: Experimental Data for a Thoriated Tungsten Cathode at 0.6 kPa

106

Chapter 7

Conclusions and Future Work

The objective of this work was to achieve a deeper understanding of the life extending
potential thoriated tungsten cathodes may have on future MPD thruster development.
The large contrast in erosion rates witnessed in the thoriated and pure tungsten cathodes
ran under these experimental conditions undoubtedly show how drastically the profile of
thorium surface coverage can affect cathode longevity.
Two separate diagnostic techniques (optical pyrometry and CCD camera imaging)
have been performed on both pure and thoriated tungsten cathodes exposed to a 20 - 60 A
plasma arc discharge in an attempt to reveal typical cathode surface axial temperature
profiles. In general, for both types of cathodes, the temperature reaches a maximum very
near the cathode tip and steadily declines towards the base, with the maximum
temperature in pure tungsten cathodes approaching the melting point of the metal.
Thoriated tungsten cathodes showed significantly less erosion with time which can be
attributed to a significantly lower work function. An analysis of the typical locations of
the peak operating temperature in pure tungsten cathodes has shown that the common
cathode failure mechanism of premature erosion is substantially more likely to occur at
107
that location. No such obvious area of concentrated erosion was witnessed in thoriated
tungsten cathodes, even after substantially longer run periods.
SEM magnification of the surface of thoriated tungsten cathodes have revealed
images illustrating substantial coverage of thorium. Since predicting the emission
capability of thoriated tungsten cathodes requires accurate specification of the coverage,
the time rate of change of the local coverage is of great value. Change in the coverage is
determined by a series of rate steps including: The rate at which thoria in the interior is
reduced and how rapidly the resultant thorium diffuses to the surface, the time scale in
which absorbed thorium is lost by surface migration or evaporation, and how readily it is
transported into the ambient gas or plasma. This research acts to be a starting point for a
more complete analysis into the changing thorium surface coverage in cathodes exposed
to a high current arc discharge.
Langmuir probing cataloging the electron temperature and plasma density in the
far plasma environment as well as near the active zone was employed. The trends and
values recorded provide the necessary boundary conditions in the construction of solid
cathode models currently being developed. Such models will be capable of predicting
erosion rates and thus cathode lifetimes, an essential component for the design of
spaceflight ready cathodes equipped to serve on future deep space and interplanetary
missions.
To further complete the analysis of the thoriated tungsten cathode surface work
function distribution (in an attempt to understand how such variations effect cathode axial
temperature profiles), a technique using Kelvin probe force microscopy may be applied.
A Kelvin probe is a non-contact non-destructive vibrating capacitor device used to
108
measure the work function of conducting materials. Because location sensitive changes
in work function along the cathode were unable to be measured, a complete
understanding of whether the thorium migrational pathways observed in these
experimental studies have a repeated effect on dictating surface work function
distribution has not been accomplished. The outcome such local changes in work
function would necessarily have on cathode surface temperature profiles may provide
new insights on designing more erosion resilient thoriated tungsten cathodes.

109

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116

Appendix A Appendix A Appendix A Appendix A

State of State of State of State of the Art MPD the Art MPD the Art MPD the Art MPD Thrusters Thrusters Thrusters Thrusters

Research on MPD thrusters developed from past efforts of NASA Glenn Research Center
(GRC) on high power arcjets in the 1960’s. During that time, 30 kW class MPD thrusters
operating on various propellants such as hydrogen and lithium showed promise.
Following initial periods of excitement, MPD thruster research all but ceased and was
mainly delegated to academic institutions until the late 1980’s when it was reinvigorated
under NASA’s Space Exploration Initiative. Overall there have been two main periods of
activity: mainly a boom in the 1960’s and early 1970’s and another period of excitement
in the late 1980’s to late 1990’s as a result of modified boundary conditions. Presently,
there is ongoing effort internationally with limited research mostly being conducted by
the U.S., Germany, Russia, and Japan.
As of today, there is a widespread difference in opinion among experts as to the
effectiveness and suitability of MPD thrusters in comparison to other electric thrusters, as
there are many unanswered questions regarding the optimal operating conditions. Such
uncertainty is mainly due to the fact that many of the individual working mechanisms are
not well understood and that there is no relevant design and operating standard.
However, recent studies have shown that applied field magnetoplasmadynamic thrusters
117
(AF-MPDT) have the potential of providing specific impulses of 5000-6000 s and thrust
efficiencies greater than 50% at reasonable power levels (<500 kW’s). Thruster power
levels ranging from 2 kW to 4 MW have also been investigated and low power (<30 kW)
applied-field lithium thrusters have been operated for over 500 hours providing evidence
that slight magnetic fields can largely reduce cathode erosion and increase lifetime.
Table A.1 shows notable thruster performance recorded from various research groups.

Table A.1: Thruster Performance by Various Research Groups [35]

118
Reported in 1997, collaborative experimental studies undertaken by the Research
Institute of Applied Mechanics and Electrodynamics (RIAME) and NASA have shown
that for studies of the under 30 kW and 200 kW lithium thruster, that the tungsten
multichannel hollow cathode has demonstrated superior performance. Indeed, this and
other studies have noted similar trends in regards to optimizing thruster performance.
Such trends are noted below:

• The multi-channel hollow cathode is preferable to both single channel hollow
cathodes and solid rod cathodes [17].

• Barium additives are beneficial to cathode longevity as demonstrated in a
MAI/NASA study. Experimental results indicated that a barium additive was
responsible for an active zone reduction in temperature by 350-400 °C and an
anode reduction of 100 °C, with discharge voltages decreasing between 3-4 V
[60].

• Lithium is an ideal propellant for plasma thrusters (including MPD’s) where
frozen flow losses are important. This is due to a low first ionization potential
(5.4 eV), a high second ionization potential (75.6 eV), and a high first excitation
level (59.0 eV) of the lithium ion. Using lithium also prevents the need for high-
voltage ignition capacitors and facilities to achieve breakdown of inert gases. In
119
addition, lithium propellant combined with a multi-channel design, have been
shown to increase efficiency and thruster lifetime, by reducing the near-cathode
voltage fall and electrode erosion. Lastly, lithium has the capability of being
stored in solid form onboard spacecraft, potentially allowing for significant mass
savings [10].

• At high power ( >500 kW), depending on the magnitude of the applied field, Hall
contribution to thrust appears to reduce in importance, as the thrust tends to
remain the same as in the self-field operation. In these cases, the applied field
yields no significant performance increase. Pinch and Hall effects, which tend to
rarefy the plasma in the external region of the acceleration chamber, may be the
cause of this occurrence [48].

• Injecting propellant through the anode has been shown to improve performance
[35] and reduce electrode onset.

• High efficiencies (>30%) are only reached at high power levels (>200 kW),
MPDTs require power levels that are an order of magnitude higher than what is
currently available on spacecraft in order to be competitive with other propulsion
options [10].
120
• It appears that one of the principal hardware problems in applied field MPD
design is the magnet. With regard to overall efficiency, it is necessary to consider
the use of a permanent magnet where the maximum field strength is limited to
(<0.2 T) [36].

121

Appendix B Appendix B Appendix B Appendix B

Other Candidates for Mars Missions Other Candidates for Mars Missions Other Candidates for Mars Missions Other Candidates for Mars Missions

Although magnetoplasmadynamic thrusters show a large degree of potential for both
piloted and cargo missions to Mars, there are a host of alternative technologies that are
also being considered, particularly in the case of cargo transportation
1
. In this section, a
summary of the alternatives and their positive and negative attributes are examined.
Included in the analysis are typically high power and high specific impulse alternatives
with tolerable efficiencies and a reasonable degree of technological readiness. Many of
the included examples have been successfully characterized as laboratory thrusters with
direct measurement of thrust and efficiency and have demonstrated the potential for
achieving hours of operational lifetime without significant degradation of system
components. A few of the technologies (i.e. Hall, ion, and arcjet) have been flown in
space and are readily manufactured, while others are still in the conceptualization stage.
Note that “super advanced” concepts necessary for interstellar travel, such as antimatter
or beamed energy propulsion, were not included in this study.

1
Major portions of this appendix were taken directly from the JPL Advanced Propulsion Technology
Group notebooks distributed in the Advanced Spacecraft Propulsion course at the University of Southern
California. Used here with permission.
122
Hall Thrusters

Hall thrusters are relatively simple devices consisting of a cylindrical channel with an
interior anode, a magnetic circuit that generates a primarily radial magnetic field across
the channel, and a cathode external to the channel. The channel is closed at one end,
where an annular anode is situated. The other end of the channel is open and forms the
exit path for the accelerated ions. Outside the channel, beyond the exit for the ion stream,
is an external cathode. As the electrons emitted by the cathode move towards the anode
under the influence of the applied electric field, the radial magnetic field results in a force
acting on them in a direction perpendicular to the plane containing the two fields, which
causes them to drift in an azimuthal direction. This azimuthal drift results in a Hall
current and impedes the progress of the electrons towards the anode. The Hall current is
the result of the electrons gyrating around the magnetic field lines in a plane parallel to

Figure B.1: Diagram of a Hall Stationary Plasma Thruster
123
the applied electric field. A diagram of a Hall stationary plasma thruster can be seen in
figure B.1.
Studies into Hall thruster began in the United States and the former USSR in the
1950’s through part of the 1960’s. Not so long after research into these devices was
achieving some measurable success, the U.S. opted to concentrate efforts on developing
gridded ion thrusters due to the low performance and high erosion rates. As of present,
Hall thrusters have been mainly used for in-space applications including orbit raising, on-
orbit maneuvers, and de-orbit functions.
Hall thrusters operate nominally in the 1500 s specific impulse regime and show
promise in the far term (with the addition of a second acceleration stage) of reaching I
sp
’s
of over 4000 s. The efficiency and specific impulse of flight-ready Hall thrusters are
typically lower than that achievable of ion thrusters, however, the thrust-to-power ratio is
higher, all while requiring fewer power sources for operation. Today, Hall thrusters are
commercially available at the 1.5 to 4.5 kW power level while research and development
into the 10 – 50 kW range is underway, with the largest power levels capable of
providing electric propulsive piloted Mars missions [47].

Ion Thrusters

Work on ion thrusters first began in the U.S. in the late 1950’s with the majority of
modern ion thrusters use xenon gas as propellant. In an ion thruster, propellant is
injected at a downstream end of the thruster and begins on a flow path toward the
upstream end. Electrons generated by a hollow cathode are attracted to the positively
124
biased chamber walls which are charged to a high potential by the thruster’s power
supply. Injected propellant is then ionized from electrons emanating from the cathode via
electron bombardment. As electrons approach the surrounding walls, appropriately
placed high strength magnets create magnetic fields which redirect the electrons into the
discharge chamber. Increasing the length of time that propellant atoms and electrons
remain in the discharge chamber increases the likely chance of ionization, thus
encouraging a more efficient ionization process. Within the thruster, ions are accelerated
by electrostatic forces generated by ion grids positioned at the downstream end of the
thruster. Within each grid, are thousands of coaxial openings which together act as a lens
that electrically focuses ions through the optics. Because the ion thruster expels a large
amount of positive ions, an equal amount of negative charge must be expelled to keep the
total charge of the exhaust beam neutral. A second neutralizing hollow cathode is located

Figure B.2: Diagram of the Underlining Processes in an Ion Thruster
125
on the downstream boundary of the thruster and expels the necessary electrons. A
diagram of a simple ion thruster can be seen in figure B.2.
After the successful flight of the ion propulsion system on Deep Space 1 (DS1),
the feasibility of using solar electric propulsion (SEP) based on modified systems utilized
on DS1, is currently being examined for prospective Mars Sample Return (MSR)
missions. Subsequent MSR studies have assumed that a single medium-class launch
vehicle consisting of a two-winged solar array capable of generating a total of 17 kW
beginning-of-life (BOL) power (at a distance of 1 AU from the sun) and equipped with a
total of four advanced NSTAR ion engines would be capable of such an endeavor [9].
Robotic missions to the outer planets employing an ion propulsion system (IPS)
composed of 60-cm diameter ion engines capable of processing 25-kW of electric power
and employing xenon as propellant with an estimated efficiency of 0.67 at a specific
impulse of 5000 s, 0.77 at 10000 s, and 0.77 at 15000 s have been considered [46]. For a
1 MW system, the vehicle mass with ion engines would be less than that for MPD
thrusters.

Arcjet Thrusters

In an arcjet thruster, a tightly constricted electric arc capable of carrying high currents
(>100 A), heats the core of an injected propellant stream to high temperatures, while the
walls of the thruster are maintained at much lower temperatures (less than 3,000 K) to
prevent melting. Because of the higher temperatures in the core, the exhaust velocity of
an arcjet can reach, or even exceed, 10 km/s, as opposed to only 4 km/s for a chemical
126
thruster [56]. Due to its simple design and high thrust density, the arcjet has become a
very attractive alternative for inclination adjustment and orbit control.
The DC arcjet has a cylindrically symmetric geometry and consists of a cathode,
an anode (which forms the plenum chamber), constrictor channel, nozzle, and a
propellant injector. In operation, a high current (up to several hundred Amperes), low
voltage (~ 100 V) arc is established in a laminar column from the cathode tip. The arc
then passes through a constrictor channel where it attaches to the anode in an axially
symmetric diffuse arc. Propellant gas is swirled into the constrictor through injection
ports located behind the cathode. Swirling is done to stabilize the arc, constrain the hot

Figure B.3: Diagram of an Arcjet Thruster
127
gas discharge column to the axis of the vortex, cool the electrodes and chamber walls,
and to bring the gas into longer and more effective contact with the arc. The constricted
current arc superheats (up to 30,000-50,000 K) and ionizes the gas on the centerline of
the constrictor, which then heats the swirling boundary gas through radiation and
conduction (resulting in a strong radial temperature gradient). This process allows the
centerline temperature of the gas to be very high without melting the nozzle. The hot
propellant is then accelerated out of the thruster through the expansion nozzle. A
diagram of an arcjet thruster can be seen in figure B.3.
It has been shown [56] that arcjets tend to not be as competitive as other electric
propulsive technologies for Mars cargo missions. For rather small dimensions and
relatively high temperatures of the flow fields, the Reynolds number is particularly low
(~10-100). Such low numbers imply significant friction and heat transfer. Therefore,
improvements is specific impulse associated with increased temperature incur lower
efficiencies at fixed power because of lower flow densities. Typical values of kilowatt
level arcjets are less than 1 N of thrust and moderate specific impulses in the range of 500
to 600 s. At fixed mass flow rates, the propellant’s ability to absorb heat limits power
dissipation in the arc discharge. Thus, the arc voltage decreases with higher current.
High-power arcjets in the range of 10-30 kW have been tested in a laboratory
setting and have been proposed for orbit raising missions and other applications of
primary propulsion [62]. However, large considerations remain whether they would be
readily useable for Mars cargo type missions.

128
Pulse Inductive Thrusters (PIT)

The pulsed inductive thruster (PIT) is a high power electromagnetic propulsion system
that can provide high thrust efficiency over a wide range of specific impulse values.
A pulsed inductive thruster uses a flat induction coil (approximately 1 m in
diameter) and a fast gas valve to inject a few milligrams of propellant over the coil. Once
the gas has been injected, a bank of high-voltage, high-energy storage capacitors is
discharged providing a large azimuthal current pulse to the coil. The time-varying
electromagnetic field caused by the current pulse ionizes the propellant gas and causes
the ionized gas to accelerate away from the coil. Because the energy is inductively
coupled into the plasma, the device can be designed so that the plasma has minimal

Figure B.4: Diagram of a Pulsed Inductive Thruster (PIT)
129
contact with thruster surfaces, resulting in minimal erosion of thruster components. A
diagram of a pulsed inductive thrusted can be seen in figure B.4.
State of the art performance measurements for the PIT were obtained by TRW
under single-shot discharge conditions. Using ammonia propellant and a 16-kV capacitor
bank charging voltage, 1 m diameter thruster efficiencies of 35% to 55% were achieved
for specific impulse values of 2000 to 8000 s, respectively. Ultimately, the specific goal
was to demonstrate a thruster efficiency of at least 60% for repetitively pulsed discharges
of 10 to 100 pulses discharged at 10 Hz or higher with peak power levels exceeding 1
MW [19].
A simple equivalent circuit model of the PIT acceleration mechanism has been
developed by TRW, while NASA Glenn Research Center has developed a physics-based
numerical model to understand and improve thruster performance. Currently, much work
is being directed toward thruster physics simulation and the PIT concept is at present not
a viable candidate as much work is still necessary to determine thruster potential and
lifetime duration.

Variable Specific Impulse Magnetoplasma Rocket (VASIMR)
Work on the Variable Specific Impulse Magnetoplasma Rocket (VASIMR) has been
underway since the early 1980s. In January 2005, the work was moved to the Ad Astra
Rocket Company located near NASA’s Johnson Space Center (JSC).
The VASIMR system utilizes an arrangement of magnetic coils which work to
produce a strong magnetic field which confines and guides hydrogen plasma while
130

Figure B.5: Diagram of the Variable Specific Impulse Magnetoplasma Rocket

insulating it from the material wall. Within the plasma injection subsystem, the pre-
ionized hydrogen propellant is injected into the device by means of a
magnetoplasmadynamic discharge. This discharge provides a source of ionized gas
which can then be further heated through a variety of wave-particle processes, including
electron and ion cyclotron resonance heating (ECRH and ICRH), as well as whistler
wave heating. In ECRH and ICRH processes, electrons and ions which are constrained
by the magnetic field, move along helical paths and are heated by the application of
electromagnetic fields at a frequency resonant with the orbital or cyclotron frequency.
Most of the heating takes place in the central cell, which acts as a power amplifier. In all
cases, plasma electrons and ions absorb energy from the incoming waves through
resonant mechanisms. As it moves downstream, the plasma enters the nozzle section
131
which converts the thermal energy of the plasma to directed kinetic energy. The plasma
is then directed out of the rocket and to provide useful thrust. A schematic of the
VASIMR system can be seen in figure B.5.
An attractive feature of the VASIMR concept is the ability to be configured for a
variation of thrust and specific impulse (although most electric thrusters are capable of
such a feat). The flexibility in thrust is due to a detachment technique that separates the
plasma from the magnetic field by collisional diffusion. In this technique, a low
temperature flow of neutral hydrogen is injected at high Mach numbers through annular
coaxial ports in the material nozzle. It is due to the injected flow (which has a radial as
well as an axial velocity component), that a relatively cool insulating boundary layer
works to protect the wall and separate the plasma from the magnetic field. This
detachment technique works at low specific impulses where the plasma density and thrust
levels are high. At high specific impulses, however, the neutral gas would be detrimental
to the high velocity, low density flow. Therefore, in this regime, a weak, high frequency
AC ripple superimposed on the higher intensity DC nozzle magnetic field induces plasma
instabilities and turbulence which lead to detachment. By controlling the aft magnetic
“gate”, it is possible to modulate the effective throat area and hence the thrust. In
addition, by controlling the exhaust gas temperature through RF power and the (pre-
ionized) hydrogen flow rate, the specific impulse can also be adjusted independently of
the thrust and power. This ability to vary the thrust and specific impulse independently
(and at constant power) enables the performance to be tailored to a specific mission to
optimize trip time, payload mass fraction, or even acceleration.
132
No end-to-end test of the complete device has been performed to date. Therefore,
based on theoretical extrapolation, these studies have assumed a somewhat optimistic
overall power efficiency of 60% and specific mass of 6 kg/kW at a power level of 10
MW. Current and future work on VASIMR includes more detailed study of the exhaust
properties such as velocity, thrust, and mass flow rate. Additional research will focus on
high density plasma injection, ICRH, ECRH, and whistler wave heating as well as the
physics of the plasma-field detachment in the magnetic nozzle. Work is also underway to
assess the feasibility of using high temperature superconducting magnets capable of
passive radiative cooling and the transition to natural superconductors at ambient space
temperatures. Such technology would enable the elimination of the active refrigeration
loops necessary with conventional superconductors, resulting in dramatic reductions in
system mass.
Preliminary work is also underway to define a possible near term, on-orbit
demonstration of such a lightweight system using high capacity, rechargeable batteries at
power levels of 50 kW (in pulses of several minutes). The potential of VASIMR to
deliver relatively high thrust (1000 - 2000 N) and high specific impulse (3000 - 30,000
lb
f
·s/lb
m
) at multi-megawatt power levels, makes it competitive with high powered
nuclear electric propulsion (NEP) systems which operate at lower thrust, and nuclear
thermal rocket (NTR) systems which have a much lower I
sp
. An attractive characteristic
of this device is the potential ability to vary thrust and specific impulse during a mission
over a wider range than a comparable power ion or MPD system. This feature could
benefit missions including high payload, low speed transits as well as lower payload,
high speed cases with the same engine platform. Whether the variable I
sp
feature is
133
ultimately a significant benefit or not will be strongly dependent on the particular mission
as well as actual values for overall efficiency and specific mass.

Nuclear Thermal Rockets

Throughout the late 1950’s to early 1970’s there was a relatively large focus on
developing nuclear thermal rockets. Approximately $9.6 billion (2010 dollars) was
invested in solid-core nuclear rocket development in the U. S. prior to 1973. This work
was directed at the manned Mars missions and concentrated on the development of large,
high-thrust engines. It is due to the significantly higher energy densities of nuclear
reactive propellant over chemical fuels (~10
7
times), that a series of engines based on
hydrogen-cooled reactor technology were built and testing during the '60s and early 70s.
Traditionally, there are three main types of nuclear thermal rockets: solid core, liquid
core, and gas core. Of the three, only a solid-core engine prototype was ever built.

Solid Core and Particle-Bed Nuclear Thermal Rocket

In the most traditional type, a solid core design, a nuclear reactor is used to heat the
working propellant moving through the reactor core. Ideally, the core of these reactors
consists of clusters of fuel elements through which hydrogen coolant is passed. In this
engine the propellant is heated as it passes through a heat-generating solid fuel core. An
expander cycle drives the turbopumps, and control drums located on the periphery of the
core control the reactivity of the reactor. Because nuclear reactions can create
134
substantially higher temperatures (more than the materials can withstand), all reactor-
based concepts are ultimately restricted by the temperature limits of their materials of
construction; thus, the specific impulse of these systems range from around 800 lb
f
·s/lb
m

Figure B.6: Diagram of a Solid-Core Nuclear Thermal Rocket
for a solid-core heat exchanger fission reactor. A diagram of a solid-core rocket engine
can be seen in figure B.6.
In 1966, the testing of the Nuclear Engine for Rocket Vehicle Application
(NERVA) began. This engine was designed to operate at 1500 MW, provide 333 kN of
thrust at a specific impulse of 825 lb
f
·s/lb
m
, and have an engine weight of 10.4 metric
tons. It was engineered for a ten hour life and sixty operating cycles. During testing,
NERVA demonstrated that nuclear thermal rocket engines were feasible for a future Mars
manned missions. However, NASA program funding began to decline after 1969 and
during the Nixon administration, in 1972, the program was terminated.
135
Another promising design that should increase specific impulse is the particle-bed
nuclear thermal rocket. In a particle-bed reactor, the nuclear fuel is in the form of a
particulate bed through which the working fluid is pumped. This permits operation at a

Figure B.7: Major Components of a Particle-Bed Nuclear Rocket Engine

higher temperature than the solid-core reactor by reducing the fuel strength requirements.
Projected performance of a particle-bed design are specific impulses of around 1000
lb
f
·s/lb
m
and thrust to weight ratios greater than one. However, such performance would
come at a significant cost in complexity. A diagram of a particle-bed nuclear rocket
engine can be seen in figure B.7.
136
Liquid Core Nuclear Thermal Rocket

Instead of using a solid reactor core, it is likely possible to use liquid fissionable material
in a rotating-drum configuration. Dramatically greater improvements are theoretically
possible by mixing the nuclear fuel into the working fluid, and allowing the reaction to
take place in the liquid mixture itself. The performance of the liquid-core rocket engine
could potentially be superior to that of the solid-core or particle-bed engine since the
propellant temperature is no longer constrained by the melting temperature of the nuclear
fuel. Specific impulses in the range of 1300-1500 lb
f
·s/lb
m
should be possible. However,
a serious limitation of the liquid-core rocket performance is the loss of fuel as a result of
droplet entrainment and vaporization. This can result in an unacceptable loss of
fissionable material in terms of cost or contamination. Figure B.8 illustrates the major
components of a liquid-core nuclear thermal rocket engine.

Figure B.8: Major Components of a Liquid-Core Nuclear Thermal Rocket Engine
137
Open-Cycle Gas-Core/Closed-Cycle Gas-Core Nuclear Thermal Rocket

At present, the highest reactor core temperature in a nuclear rocket can be achieved by
using gaseous fissionable material. However, with both the open and closed cycle
concepts, cooling the engine walls is a major engineering problem.
In a conventional open-cycle gas-core nuclear rocket (GCR), energy is produced
by a fissioning plasma which allows the core to radiate like a blackbody. By injecting a
hydrogen propellant that flows around the core and hydrodynamically containing it,
propulsion is produced by the heated, seeded hydrogen as it exits through the nozzle. It
has been shown that a specific impulse of about 1000-2000 s can be expected from the
fission gas core nuclear rocket (and at a sizable thrust) [32]. Figure B.9 shows an open-
cycle gas-core nuclear rocket engine.

Figure B.9: An Open-Cycle Gas-Core Nuclear Rocket Engine
138
The closed-cycle gas-core nuclear rocket or nuclear “light-bulb” engine avoids the
nuclear fuel loss of the open-cycle gas-core engine by containing the nuclear plasma in a
quartz capsule. In the reaction chamber, thermal radiation from the plasma passes
through the quartz capsule to be absorbed by the hydrogen propellant, while the nozzle
and quartz wall are regeneratively cooled by the hydrogen propellant. A large variety
engine capable of 6000 MW and 445 kN of thrust would weigh approximately 56.8
metric tons and have a mass fraction as low as 0.57, however, the specific impulse would
be nearly 2080 lb
f
·s/lb
m
all while having a thrust to weight ratio of near one. A small
variety engine (448 MW power, 44.7 kN thrust, 15.1 metric tons engine weight) has been
designed to be small enough to be compatible with the former Space Shuttle cargo bay
with a specific impulse of about 1550 lb
f
·s/lb
m
and a thrust to weight ratio of about 0.3.
Figure B.10 shows a closed-cycle gas-core nuclear rocket engine.

Figure B.10: A Closed-Cycle Gas-Core Nuclear Rocket Engine
139
Nuclear Pulse Propulsion

The interest in employing nuclear explosives to power spacecraft dates from the late
1940’s through the middle 1950’s when early calculations were performed at the Los
Alamos Scientific Laboratory. Soon after, the concept of nuclear pulse propulsion
emerged. In nuclear pulse propulsion, effective exhaust temperatures are possible due to
the short interaction time of the propellant with the structure of the vehicle. In this
concept fission bombs (< 0.1 kton) would be dropped at the rate of one bomb every 1 to
10 seconds and detonated at a distance of 100 to 1000 feet from the vehicle. The blast
from the explosion would interact with a pusher plate which transmits the impulse to the
spacecraft through a shock attenuation system. After compressing the shock absorbers,

Figure B.11: A Conceptual Design of a Nuclear Pulse Rocket
140
the pusher returns to its neutral position and is ready to accept the following impulse. A
conceptual design of a nuclear pulse rocket can bee seen in figure B.11. Any desired
total vehicle velocity is acquired by varying the total number of pulse units expended.
The propellant/pusher interaction times range under one millisecond. Therefore, the total
"operating time" of propellant interaction for even a high mission velocity may be under
one second. Fission pulse propulsion was the conceptual basis of the most prominent
study into nuclear pulse propulsion, the ORION project of the mid 1960’s.
However, at the conclusion of the project many challenges were still not
addressed, including: The concern of radiation damage to nearby space vehicles due to
neutron and gamma-ray radiation from the high-energy pulses, the impractically large
spacecraft mass, and the very real issue of international political resistance to a vehicle
equipped with thousands of potential weapons in orbit. Such resistance ultimately made
the concept infeasible, yet an appropriate launching point for more practical nuclear
propulsion concepts.

Abstract (if available)

Abstract Since the early to mid 1960’s, laboratory studies have demonstrated the unique ability of magnetoplasmadynamic (MPD) thrusters to deliver an exceptionally high level of specific impulse and thrust at large power processing densities. These intrinsic advantages are why MPD thrusters have been identified as a prime candidate for future long duration space missions, including piloted Mars, Mars cargo, lunar cargo, and other missions beyond low Earth orbit (LEO). The large total impulse requirements inherent of the long duration space missions demand the thruster to operate for a significant fraction of the mission burn time while requiring the cathodes to operate at 50 to 10,000 kW for 2,000 to 10,000 hours. The high current levels lead to high operational temperatures and a corresponding steady depletion of the cathode material by evaporation. This mechanism has been identified as the life-limiting component of MPD thrusters. ❧ In this research, utilizing subscale geometries, time dependent cathode axial temperature profiles under varying current levels (20 to 60 A) and argon gas mass flow rates (450 to 640 sccm) for both pure and thoriated solid tungsten cathodes were measured by means of both optical pyrometry and charged-coupled (CCD) camera imaging. Thoriated tungsten cathode axial temperature profiles were compared against those of pure tungsten to demonstrate the large temperature reducing effect lowered work function imparts by encouraging increased thermionic electron emission from the cathode surface. Also, Langmuir probing was employed to measure the electron temperature, electron density, and plasma potential near the “active zone” (the surface area of the cathode responsible for approximately 70% of the emitted current) in order to characterize the plasma environment and verify future model predictions. ❧ The time changing surface microstructure and elemental composition of the thoriated tungsten cathodes were analyzed using a scanning electron microscope (SEM) in conjunction with energy-dispersive X-ray spectroscopy (EDS). Such studies have provided a qualitative understanding of the typical pathways in which thorium diffuses and how it is normally redistributed along the cathode surface. ❧ Lastly, the erosion rates of both pure and thoriated tungsten cathodes were measured after various run times by use of an analytical scale. These measurements have revealed the ability of thoriated tungsten cathodes to run as long as that of pure tungsten but with significantly less material erosion.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Codron, Douglas A. (author)

Core Title An experimental investigation of cathode erosion in high current magnetoplasmadynamic arc discharges

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Astronautical Engineering

Publication Date 07/06/2012

Defense Date 04/13/2012

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag arc discharge,cathode,electric propulsion,magntoplasmadynamic thruster,OAI-PMH Harvest,plasma,space

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Erwin, Daniel A. (committee chair), Goodfellow, Keith (committee member), Muntz, E. Phillip (committee member), Wang, Joseph (committee member)

Creator Email dcodron@usc.edu,dooglas50@hotmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-52633

Unique identifier UC11289105

Identifier usctheses-c3-52633 (legacy record id)

Legacy Identifier etd-CodronDoug-916.pdf

Dmrecord 52633

Document Type Dissertation

Rights Codron, Douglas A.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA